Log in

Relevant bibliographies by topics / Algebra, Abstract / Journal articles

To see the other types of publications on this topic, follow the link: Algebra, Abstract.

Journal articles on the topic 'Algebra, Abstract'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 July 2024

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Algebra, Abstract.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Sreeja S Nair, Kumari. "Exploring Normal Covering Spaces: A Bridge between Algebraic Topology and Abstract Algebra." International Journal of Science and Research (IJSR) 12, no. 8 (August 5, 2023): 2474–77. http://dx.doi.org/10.21275/sr23824225856.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

SAMEA, H. "ESSENTIAL AMENABILITY OF ABSTRACT SEGAL ALGEBRAS." Bulletin of the Australian Mathematical Society 79, no. 2 (March 13, 2009): 319–25. http://dx.doi.org/10.1017/s0004972708001329.

Full text

Abstract:

AbstractA number of well-known results of Ghahramani and Loy on the essential amenability of Banach algebras are generalized. It is proved that a symmetric abstract Segal algebra with respect to an amenable Banach algebra is essentially amenable. Applications to locally compact groups are given.

APA, Harvard, Vancouver, ISO, and other styles

3

Chen, Quanguo, and Yong Deng. "Hopf algebra structures on generalized quaternion algebras." Electronic Research Archive 32, no. 5 (2024): 3334–62. http://dx.doi.org/10.3934/era.2024154.

Full text

Abstract:

<abstract><p>In this paper, we use elementary linear algebra methods to explore possible Hopf algebra structures within the generalized quaternion algebra. The sufficient and necessary conditions that make the generalized quaternion algebra a Hopf algebra are given. It is proven that not all of the generalized quaternion algebras have Hopf algebraic structures. When the generalized quaternion algebras have Hopf algebraic structures, we describe all the Hopf algebra structures. Finally, we shall prove that all the Hopf algebra structures on the generalized quaternion algebras are isomorphic to Sweedler Hopf algebra, which is consistent with the classification of 4-dimensional Hopf algebras.</p></abstract>

APA, Harvard, Vancouver, ISO, and other styles

4

Benkart, Georgia, and I. N. Herstein. "Abstract Algebra." American Mathematical Monthly 94, no. 8 (October 1987): 804. http://dx.doi.org/10.2307/2323434.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Freedman, Haya, G. D. Crown, M. H. Fenrick, and R. J. Valenza. "Abstract Algebra." Mathematical Gazette 71, no. 455 (March 1987): 89. http://dx.doi.org/10.2307/3616329.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Madden, Daniel J., Ronald Solomon, and Ronald S. Irving. "Abstract Algebra." American Mathematical Monthly 112, no. 5 (May 1, 2005): 475. http://dx.doi.org/10.2307/30037513.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Sharma, Vibhuti. "Abstract Algebra." International Journal for Research in Applied Science and Engineering Technology 9, no. VII (July 20, 2021): 1628–34. http://dx.doi.org/10.22214/ijraset.2021.36688.

Full text

Abstract:

Ring hypothesis is one of the pieces of the theoretical polynomial math that has been thoroughly used in pictures. Nevertheless, ring hypothesis has not been associated with picture division. In this paper, we propose another rundown of similarity among pictures using rings and the entropy work. This new record was associated as another stopping standard to the Mean Shift Iterative Calculation with the goal to accomplish a predominant division. An examination on the execution of the calculation with this new ending standard is finished. In spite of the fact that ring hypothesis and class hypothesis from the start sought after assorted direction it turned out during the 1970s – that the investigation of functor groupings furthermore reveals new plots for module hypothesis.

APA, Harvard, Vancouver, ISO, and other styles

8

Bai, Liqian, Xueqing Chen, Ming Ding, and Fan Xu. "A generalized quantum cluster algebra of Kronecker type." Electronic Research Archive 32, no. 1 (2024): 670–85. http://dx.doi.org/10.3934/era.2024032.

Full text

Abstract:

<abstract><p>The notion of generalized quantum cluster algebras was introduced as a natural generalization of Berenstein and Zelevinsky's quantum cluster algebras as well as Chekhov and Shapiro's generalized cluster algebras. In this paper, we focus on a generalized quantum cluster algebra of Kronecker type which possesses infinitely many cluster variables. We obtain the cluster multiplication formulas for this algebra. As an application of these formulas, a positive bar-invariant basis is explicitly constructed. Both results generalize those known for the Kronecker cluster algebra and quantum cluster algebra.</p></abstract>

APA, Harvard, Vancouver, ISO, and other styles

9

Huang, Junyuan, Xueqing Chen, Zhiqi Chen, and Ming Ding. "On a conjecture on transposed Poisson $ n $-Lie algebras." AIMS Mathematics 9, no. 3 (2024): 6709–33. http://dx.doi.org/10.3934/math.2024327.

Full text

Abstract:

<abstract><p>The notion of a transposed Poisson $ n $-Lie algebra has been developed as a natural generalization of a transposed Poisson algebra. It was conjectured that a transposed Poisson $ n $-Lie algebra with a derivation gives rise to a transposed Poisson $ (n+1) $-Lie algebra. In this paper, we focus on transposed Poisson $ n $-Lie algebras. We have obtained a rich family of identities for these algebras. As an application of these formulas, we provide a construction of $ (n+1) $-Lie algebras from transposed Poisson $ n $-Lie algebras with derivations under a certain strong condition, and we prove the conjecture in these cases.</p></abstract>

APA, Harvard, Vancouver, ISO, and other styles

10

Bezhanishvili, Guram, and Patrick J. Morandi. "Profinite Heyting Algebras and Profinite Completions of Heyting Algebras." gmj 16, no. 1 (March 2009): 29–47. http://dx.doi.org/10.1515/gmj.2009.29.

Full text

Abstract:

Abstract This paper surveys recent developments in the theory of profinite Heyting algebras (resp. bounded distributive lattices, Boolean algebras) and profinite completions of Heyting algebras (resp. bounded distributive lattices, Boolean algebras). The new contributions include a necessary and sufficient condition for a profinite Heyting algebra (resp. bounded distributive lattice) to be isomorphic to the profinite completion of a Heyting algebra (resp. bounded distributive lattice). This results in simple examples of profinite bounded distributive lattices that are not isomorphic to the profinite completion of any bounded distributive lattice. We also show that each profinite Boolean algebra is isomorphic to the profinite completion of some Boolean algebra. It is still an open question whether each profinite Heyting algebra is isomorphic to the profinite completion of some Heyting algebra.

APA, Harvard, Vancouver, ISO, and other styles

11

Rump, Wolfgang. "Non-commutative effect algebras, L-algebras, and local duality." Mathematica Slovaca 74, no. 2 (April 1, 2024): 451–68. http://dx.doi.org/10.1515/ms-2024-0034.

Full text

Abstract:

Abstract GPE-algebras were introduced by Dvurečenskij and Vetterlein as unbounded pseudo-effect algebras. Recently, they have been characterized as partial L-algebras with local duality. In the present paper, GPE-algebras with an everywhere defined L-algebra operation are investigated. For example, linearly ordered GPE-algebra are of that type. They are characterized by their self-similar closures which are represented as negative cones of totally ordered groups. More generally, GPE-algebras with an everywhere defined multiplication are identified as negative cones of directed groups. If their partial L-algebra structure is globally defined, the enveloping group is lattice-ordered. For any self-similar L-algebra A, exponent maps are introduced, generalizing conjugation in the structure group. It is proved that the exponent maps are L-algebra automorphisms of A if and only if A is a GPE-algebra. As an application, a new characterization of cone algebras is obtained. Lattice GPE-algebras are shown to be equivalent to ∧-closed L-algebras with local duality.

APA, Harvard, Vancouver, ISO, and other styles

12

Bavula, V. V. "The generalized Weyl Poisson algebras and their Poisson simplicity criterion." Letters in Mathematical Physics 110, no. 1 (September 27, 2019): 105–19. http://dx.doi.org/10.1007/s11005-019-01214-7.

Full text

Abstract:

Abstract A new large class of Poisson algebras, the class of generalized Weyl Poisson algebras, is introduced. It can be seen as Poisson algebra analogue of generalized Weyl algebras or as giving a Poisson structure to (certain) generalized Weyl algebras. A Poisson simplicity criterion is given for generalized Weyl Poisson algebras, and an explicit description of the Poisson centre is obtained. Many examples are considered (e.g. the classical polynomial Poisson algebra in 2n variables is a generalized Weyl Poisson algebra).

APA, Harvard, Vancouver, ISO, and other styles

13

Saitô, Kazuyuki. "The regular completion of a C*-algebra with large projections." Quarterly Journal of Mathematics 70, no. 3 (May 15, 2019): 999–1007. http://dx.doi.org/10.1093/qmath/haz014.

Full text

Abstract:

Abstract When a unital C*-algebra A is prime and has very large projections, it is shown that the regular completion A^ of the algebra A is a simple, wild type III AW*-factor that has no non-zero σ-finite projections. For example, the Weaver algebra, the Crabb algebra and the Katsura algebra are prime C*-algebras that have very large projections. As a corollary, such algebras have no non-zero abelian elements, that is, they are not of type I.

APA, Harvard, Vancouver, ISO, and other styles

14

Almutiben, Nouf, Edward L. Boone, Ryad Ghanam, and G. Thompson. "Classification of the symmetry Lie algebras for six-dimensional co-dimension two Abelian nilradical Lie algebras." AIMS Mathematics 9, no. 1 (2023): 1969–96. http://dx.doi.org/10.3934/math.2024098.

Full text

Abstract:

<abstract><p>In this paper, we consider the symmetry algebra of the geodesic equations of the canonical connection on a Lie group. We mainly consider the solvable indecomposable six-dimensional Lie algebras with co-dimension two abelian nilradical that have an abelian complement. In dimension six, there are nineteen such algebras, namely, $ A_{6, 1} $–$ A_{6, 19} $ in Turkowski's list. For each algebra, we give the geodesic equations, a basis for the symmetry Lie algebra in terms of vector fields, and finally we identify the symmetry Lie algebra from standard lists.</p></abstract>

APA, Harvard, Vancouver, ISO, and other styles

15

Al-shami, Tareq M., Zanyar A. Ameen, and Abdelwaheb Mhemdi. "The connection between ordinary and soft $ \sigma $-algebras with applications to information structures." AIMS Mathematics 8, no. 6 (2023): 14850–66. http://dx.doi.org/10.3934/math.2023759.

Full text

Abstract:

<abstract><p>The paper presents a novel analysis of interrelations between ordinary (crisp) $ \sigma $-algebras and soft $ \sigma $-algebras. It is known that each soft $ \sigma $-algebra produces a system of crisp (parameterized) $ \sigma $-algebras. The other way round is also possible. That is to say, one can generate a soft $ \sigma $-algebra from a system of crisp $ \sigma $-algebras. Different methods of producing soft $ \sigma $-algebras are discussed by implementing two formulas. It is demonstrated how these formulas can be used in practice with the aid of some examples. Furthermore, we study the fundamental properties of soft $ \sigma $-algebras. Lastly, we show that elements of a soft $ \sigma $-algebra contain information about a specific event.</p></abstract>

APA, Harvard, Vancouver, ISO, and other styles

16

Zhao, Ranran. "Congruences and subdirect decompositions in universal algebra." Journal of Physics: Conference Series 2634, no. 1 (November 1, 2023): 012008. http://dx.doi.org/10.1088/1742-6596/2634/1/012008.

Full text

Abstract:

Abstract In this paper, we will focus on the topic of congruences and factorizations in universal algebra. We will first provide an introduction to universal algebra by defining lattices, algebras, congruences and other core structures. Next, we will explore the congruence and factorization properties of an algebra. Then, Birkhoff theorem indicates that every algebra can be embedded into a product of subdirectly irreducible algebras. Based on these fundamental concepts, Heyting algebra will be discussed as a typical example in universal algebra. The one-to-one correspondence between filters and congruences of a Heyting algebra will be proved. Lastly, we will show a specific way to justify the subdirectly irreducibility of a Heyting algebra.

APA, Harvard, Vancouver, ISO, and other styles

17

Piciu, Dana, Christina Theresia Dan, and Anca Dina. "Gődel filters in residuated lattices." Analele Universitatii "Ovidius" Constanta - Seria Matematica 29, no. 1 (March 1, 2021): 183–200. http://dx.doi.org/10.2478/auom-2021-0012.

Full text

Abstract:

Abstract In this paper, in the spirit of [4], we study a new type of filters in residuated lattices : Gődel filters. So, we characterize the filters for which the quotient algebra that is constructed via these filters is a Gődel algebra and we establish the connections between these filters and other types of filters. Using Gődel filters we characterize the residuated lattices which are Gődel algebras. Also, we prove that a residuated lattice is a Gődel algebra (divisible residuated lattice, MTL algebra, BL algebra) if and only if every filter is a Gődel filter (divisible filter, MTL filter, BL filter). Finally, we present some results about injective Gődel algebras showing that complete Boolean algebras are injective objects in the category of Gődel algebras.

APA, Harvard, Vancouver, ISO, and other styles

18

Ciungu, Lavinia Corina. "Weak pseudo-BCK algebras." Mathematica Slovaca 68, no. 6 (December 19, 2018): 1327–38. http://dx.doi.org/10.1515/ms-2017-0183.

Full text

Abstract:

Abstract In this paper we define and study the weak pseudo-BCK algebras as generalizations of weak BCK-algebras, extending some results given by Cı⃖rulis for weak BCK-algebras. We give some characterizations of weak pseudo-BCK algebras and we prove that a weak pseudo-BCK algebra satisfying the right distribution laws is a BCK-algebra. We define the class of commutative weak pseudo-BCK algebras, and we give equivalent definitions and characterization theorems for commutative weak pseudo-BCK algebras. The classes of quasi pseudo-BCK algebras and weak pseudo-BCK(E) algebras are introduced and a characterization theorem for quasi pseudo-BCK algebras is given. We prove that any weak pseudo-BCK(E) algebra is a pseudo-BE algebra and the class of commutative weak pseudo-BCK(E) algebras is equivalent to the class of commutative pseudo-BCK algebras.

APA, Harvard, Vancouver, ISO, and other styles

19

Brown, Lawrence G., James A. Mingo, and Nien-Tsu Shen. "Quasi-Multipliers and Embeddings of Hilbert C*-Bimodules." Canadian Journal of Mathematics 46, no. 06 (December 1994): 1150–74. http://dx.doi.org/10.4153/cjm-1994-065-5.

Full text

Abstract:

Abstract This paper considers Hilbert C*-bimodules, a slight generalization of imprimitivity bimodules which were introduced by Rieffel [20]. Brown, Green, and Rieffel [7] showed that every imprimitivity bimodule X can be embedded into a certain C*-algebra L, called the linking algebra of X. We consider arbitrary embeddings of Hilbert C*-bimodules into C*-algebras; i.e. we describe the relative position of two arbitrary hereditary C*-algebras of a C*-algebra, in an analogy with Dixmier's description [10] of the relative position of two subspaces of a Hilbert space. The main result of this paper (Theorem 4.3) is taken from the doctoral dissertation of the third author [22], although the proof here follows a different approach. In Section 1 we set out the definitions and basic properties (mostly folklore) of Hilbert C*-bimodules. In Section 2 we show how every quasi-multiplier gives rise to an embedding of a bimodule. In Section 3 we show that , the enveloping C*-algebra of the C*-algebraA with its product perturbed by a positive quasi-multiplier , is isomorphic to the closure (Proposition 3.1). Section 4 contains the main theorem (4.3), and in Section 5 we explain the analogy with the relative position of two subspaces of a Hilbert spaces and present some complements.

APA, Harvard, Vancouver, ISO, and other styles

20

Kandelaki, T. "On the Universal C*-Algebra Generated by Partial Isometry." gmj 5, no. 4 (August 1998): 333–40. http://dx.doi.org/10.1515/gmj.1998.333.

Full text

Abstract:

Abstract A universal C*-algebra is constructed which is generated by a partial isometry. Using grading on this algebra we construct an analog of Cuntz algebras which gives a homotopical interpretation of KK-groups. It is proved that this algebra is homotopy equivalent up to stabilization by 2×2 matrices to M 2(C). Therefore those algebras are KK-isomorphic.

APA, Harvard, Vancouver, ISO, and other styles

21

Hu, Xianguo. "Universal enveloping Hom-algebras of regular Hom-Poisson algebras." AIMS Mathematics 7, no. 4 (2022): 5712–27. http://dx.doi.org/10.3934/math.2022316.

Full text

Abstract:

<abstract><p>In this paper, we introduce universal enveloping Hom-algebras of Hom-Poisson algebras. Some properties of universal enveloping Hom-algebras of regular Hom-Poisson algebras are discussed. Furthermore, in the involutive case, it is proved that the category of involutive Hom-Poisson modules over an involutive Hom-Poisson algebra $ A $ is equivalent to the category of involutive Hom-associative modules over its universal enveloping Hom-algebra $ U_{eh}(A) $.</p></abstract>

APA, Harvard, Vancouver, ISO, and other styles

22

Meyer, Ralf, and Devarshi Mukherjee. "Dagger completions and bornological torsion-freeness." Quarterly Journal of Mathematics 70, no. 3 (June 5, 2019): 1135–56. http://dx.doi.org/10.1093/qmath/haz012.

Full text

Abstract:

Abstract We define a dagger algebra as a bornological algebra over a discrete valuation ring with three properties that are typical of Monsky–Washnitzer algebras, namely, completeness, bornological torsion-freeness and a certain spectral radius condition. We study inheritance properties of the three properties that define a dagger algebra. We describe dagger completions of bornological algebras in general and compute some non-commutative examples.

APA, Harvard, Vancouver, ISO, and other styles

23

Abram, J., P. B. Bhattacharya, S. K. Jain, and S. R. Nagpaul. "Basic Abstract Algebra." Mathematical Gazette 71, no. 455 (March 1987): 90. http://dx.doi.org/10.2307/3616330.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Baylis, John, and Joseph A. Gallian. "Contemporary Abstract Algebra." Mathematical Gazette 75, no. 473 (October 1991): 374. http://dx.doi.org/10.2307/3619533.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Freedman, Haya, and M. L. Curtis. "Abstract Linear Algebra." Mathematical Gazette 75, no. 473 (October 1991): 375. http://dx.doi.org/10.2307/3619534.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Fletcher, Colin R., R. Lidl, and G. Pilz. "Applied Abstract Algebra." Mathematical Gazette 70, no. 453 (October 1986): 246. http://dx.doi.org/10.2307/3615715.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Hee Lee, Hun, and Sang-gyun Youn. "New Deformations of Convolution Algebras and Fourier Algebras on Locally Compact Groups." Canadian Journal of Mathematics 69, no. 02 (April 2017): 434–52. http://dx.doi.org/10.4153/cjm-2016-027-7.

Full text

Abstract:

Abstract In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some information about the underlying groups by examining Banach algebra properties of deformed algebras. More precisely, we focus on representability as an operator algebra of deformed convolution algebras on compact connected Lie groups with connection to the real dimension of the underlying group. Similarly, we investigate complete representability as an operator algebra of deformed Fourier algebras on some ûnitely generated discrete groups with connection to the growth rate of the group.

APA, Harvard, Vancouver, ISO, and other styles

28

Leivant, Daniel, and Jean-Yves Marion. "Primitive recursion in the abstract." Mathematical Structures in Computer Science 30, no. 1 (January 2020): 33–43. http://dx.doi.org/10.1017/s0960129519000112.

Full text

Abstract:

AbstractRecurrence can be used as a function definition schema for any nontrivial free algebra, yielding the same computational complexity in all cases. We show that primitive-recursive computing is in fact independent of free algebras altogether, and can be characterized by a generic programming principle, namely the control of iteration by the depletion of finite components of the underlying structure.

APA, Harvard, Vancouver, ISO, and other styles

29

Badawy, Abd El-Mohsen, and Alaa Helmy. "Permutabitity of principal $ MS $-algebras." AIMS Mathematics 8, no. 9 (2023): 19857–75. http://dx.doi.org/10.3934/math.20231012.

Full text

Abstract:

<abstract><p>In this paper, we continue to introduce new properties of principal $ MS $-algebras deal with congruence relations via $ MS $-congruence pairs. Necessary and sufficient conditions for a pair of congruences $ (\theta_{1}, \theta_{2})\in Con(L^{\circ\circ})\times Con_{lat}(D(L)) $ to become an $ MS $-congruence pair of a principal $ MS $-algebra (principal Stone algebra) $ L $ are obtained. We describe the lattice of all $ MS $-congruence pairs of a principal $ MS $-algebra $ L $ which induced by the Boolean elements of $ L $. We introduce certain special congruence $ \Psi $ on a principal $ MS $-algebra and its related properties which are useful for the topic of this paper. A characterization of $ 2 $-permutable congruences using $ MS $-congruence pairs of principal $ MS $-algebras is established. Finally, a characterization of $ n $-permutability of congruences of principal $ MS $-algebras is given, which is a generalization of the characterization of $ 2 $-permutability of congruences of such algebras.</p></abstract>

APA, Harvard, Vancouver, ISO, and other styles

30

Borzooei, R. A., Akefe Radfar, and Sogol Niazian. "Relationship Between Hyper MV -algebras and Hyperlattices." Annals of West University of Timisoara - Mathematics and Computer Science 54, no. 2 (December 1, 2016): 75–94. http://dx.doi.org/10.1515/awutm-2016-0016.

Full text

Abstract:

Abstract Sh. Ghorbani, et al. [9], generalized the concept of MV -algebras and defined the notion of hyper MV -algebras. Now, in this paper, we try to prove that any hyper MV -algebra is a hyperlattice. First we prove that any hyper MV -algebra that satisfies the semi negation property is a hyperlattice. Then with a computer program, we show that any hyper MV -algebra of order less than 6, is a hyperlattice. Finally, we claim that this result is correct for any hyper MV -algebra.

APA, Harvard, Vancouver, ISO, and other styles

31

ALAGHMANDAN, MAHMOOD, RASOUL NASR-ISFAHANI, and MEHDI NEMATI. "CHARACTER AMENABILITY AND CONTRACTIBILITY OF ABSTRACT SEGAL ALGEBRAS." Bulletin of the Australian Mathematical Society 82, no. 2 (August 4, 2010): 274–81. http://dx.doi.org/10.1017/s0004972710000286.

Full text

Abstract:

AbstractLet ℬ be an abstract Segal algebra with respect to 𝒜. For a nonzero character ϕ on 𝒜, we study ϕ-amenability, and ϕ-contractibility of 𝒜 and ℬ. We then apply these results to abstract Segal algebras related to locally compact groups.

APA, Harvard, Vancouver, ISO, and other styles

32

Loday, J. L., and T. Pirashvili. "The Tensor Category of Linear Maps and Leibniz Algebras." gmj 5, no. 3 (June 1998): 263–76. http://dx.doi.org/10.1515/gmj.1998.263.

Full text

Abstract:

Abstract We equip the category of linear maps of vector spaces with a tensor product which makes it suitable for various constructions related to Leibniz algebras. In particular, a Leibniz algebra becomes a Lie object in and the universal enveloping algebra functor UL from Leibniz algebras to associative algebras factors through the category of cocommutative Hopf algebras in . This enables us to prove a Milnor–Moore type theorem for Leibniz algebras.

APA, Harvard, Vancouver, ISO, and other styles

33

Tomiuk, B. J. "Isomorphisms of multiplier algebras." Glasgow Mathematical Journal 28, no. 1 (January 1986): 73–77. http://dx.doi.org/10.1017/s0017089500006364.

Full text

Abstract:

Let A and B be semisimple Banach algebras, and let M1(A) (resp. M1(B)) be the algebra of left multipliers on A (resp. B). Suppose that A is an abstract Segal algebra in B. We find conditions on A and B which imply that M1(A) is topologically algebra isomorphic to M1(B). As a special case we obtain the result of [8] which states that if A is an A*-algebra that is a*-ideal in its B*-algebra completion B and A2 is dense in A then M1(A) is topologically algebra isomorphic to M1(B). We make an application of our main result to right complemented Banach algebras.

APA, Harvard, Vancouver, ISO, and other styles

34

Mohammadzadeh, Elahe, and Rajab Ali Borzooei. "Engel, Nilpotent and Solvable BCI-algebras." Analele Universitatii "Ovidius" Constanta - Seria Matematica 27, no. 1 (March 1, 2019): 169–92. http://dx.doi.org/10.2478/auom-2019-0009.

Full text

Abstract:

Abstract In this paper, we define the concepts of Engel, nilpotent and solvable BCI-algebras and investigate some of their properties. Specially, we prove that any BCK-algebra is a 2-Engel. Then we define the center of a BCI-algebra and prove that in a nilpotent BCI-algebra X, each minimal closed ideal of X is contained in the center of X. In addition, with some conditions, we show that every finite BCI-algebra is solvable. Finally, we investigate the relations among Engel, nilpotent and solvable BCI(BCK)-algebras.

APA, Harvard, Vancouver, ISO, and other styles

35

Liu, Ling, Abdenacer Makhlouf, Claudia Menini, and Florin Panaite. "BiHom-pre-Lie algebras, BiHom-Leibniz algebras and Rota–Baxter operators on BiHom-Lie algebras." Georgian Mathematical Journal 28, no. 4 (July 1, 2021): 581–94. http://dx.doi.org/10.1515/gmj-2021-2094.

Full text

Abstract:

Abstract We contribute to the study of Rota–Baxter operators on types of algebras other than associative and Lie algebras. If A is an algebra of a certain type and R is a Rota–Baxter operator on A, one can define a new multiplication on A by means of R and the previous multiplication and ask under what circumstances the new algebra is of the same type as A. Our first main result deals with such a situation in the case of BiHom-Lie algebras. Our second main result is a BiHom analogue of Aguiar’s theorem that shows how to obtain a pre-Lie algebra from a Rota–Baxter operator of weight zero on a Lie algebra. The BiHom analogue does not work for BiHom-Lie algebras, but for a new concept we introduce here, called left BiHom-Lie algebra, at which we arrived by defining first the BiHom version of Leibniz algebras.

APA, Harvard, Vancouver, ISO, and other styles

36

Almutiben, Nouf, Ryad Ghanam, G. Thompson, and Edward L. Boone. "Symmetry analysis of the canonical connection on Lie groups: six-dimensional case with abelian nilradical and one-dimensional center." AIMS Mathematics 9, no. 6 (2024): 14504–24. http://dx.doi.org/10.3934/math.2024705.

Full text

Abstract:

<abstract><p>In this article, the investigation into the Lie symmetry algebra of the geodesic equations of the canonical connection on a Lie group was continued. The key ideas of Lie group, Lie algebra, linear connection, and symmetry were quickly reviewed. The focus was on those Lie groups whose Lie algebra was six-dimensional solvable and indecomposable and for which the nilradical was abelian and had a one-dimensional center. Based on the list of Lie algebras compiled by Turkowski, there were eight algebras to consider that were denoted by $ A_{6, 20} $–$ A_{6, 27} $. For each Lie algebra, a comprehensive symmetry analysis of the system of geodesic equations was carried out. For each symmetry Lie algebra, the nilradical and a complement to the nilradical inside the radical, as well as a semi-simple factor, were identified.</p></abstract>

APA, Harvard, Vancouver, ISO, and other styles

37

GHAHRAMANI, F., and A. T. M. LAU. "Weak amenability of certain classes of Banach algebras without bounded approximate identities." Mathematical Proceedings of the Cambridge Philosophical Society 133, no. 2 (September 2002): 357–71. http://dx.doi.org/10.1017/s0305004102005960.

Full text

Abstract:

In a recent paper [3] Dales and Pandey have shown that the class Sp of Segal algebras is weakly amenable. In this paper, for various classes of Segal algebras, we characterize derivations and multipliers from a Segal algebra into itself and into its dual module. In particular, we prove that every Segal algebra on a locally compact abelian group is weakly amenable and an abstract Segal subalgebra of a commutative weakly amenable Banach algebra is weakly amenable. We also introduce the Lebesgue–Fourier algebra of a locally compact group G and study its Arens regularity when G is discrete or compact.

APA, Harvard, Vancouver, ISO, and other styles

38

Bezushchak, O. O., and B. V. Oliynyk. "Algebraic theory of measure algebras." Reports of the National Academy of Sciences of Ukraine, no. 2 (May 3, 2023): 3–9. http://dx.doi.org/10.15407/dopovidi2023.02.003.

Full text

Abstract:

A. Horn and A. Tarski initiated the abstract theory of measure algebras. Independently V. Sushchansky, B. Oliynyk and P. Cameron studied the direct limits of Hamming spaces. In the current paper, we introduce new examples of locally standard measure algebras and complete the classification of countable locally standard measure algebras. Countable unital locally standard measure algebras are in one-to-one correspondence with Steinitz numbers. Given a Steinitz number s such measure algebra is isomorphic to the Boolean algebra of s-periodic sequences of 0 and 1. Nonunital locally standard measure algebras are parametrized by pairs (s, r), where s is a Steinitz number and r is a real number greater or equal to 1. We also show that an arbitrary (not necessarily locally standard) measure algebra is embeddable in a metric ultraproduct of standard Hamming spaces. In other words, an arbitrary measure algebra is sofic.

APA, Harvard, Vancouver, ISO, and other styles

39

Xu, Senrong, Wei Wang, and Jia Zhao. "Twisted Rota-Baxter operators on Hom-Lie algebras." AIMS Mathematics 9, no. 2 (2023): 2619–40. http://dx.doi.org/10.3934/math.2024129.

Full text

Abstract:

<abstract><p>Uchino initiated the investigation of twisted Rota-Baxter operators on associative algebras. Relevant studies have been extensive in recent times. In this paper, we introduce the notion of a twisted Rota-Baxter operator on a Hom-Lie algebra. By utilizing higher derived brackets, we establish an explicit $ L_{\infty} $-algebra whose Maurer-Cartan elements are precisely twisted Rota-Baxter operators on Hom-Lie algebra s. Additionally, we employ Getzler's technique of twisting $ L_\infty $-algebras to establish the cohomology of twisted Rota-Baxter operators. We demonstrate that this cohomology can be regarded as the Chevalley-Eilenberg cohomology of a specific Hom-Lie algebra with coefficients in an appropriate representation. Finally, we study the linear and formal deformations of twisted Rota-Baxter operators by using the cohomology defined above. We also show that the rigidity of a twisted Rota-Baxter operator can be derived from Nijenhuis elements associated with a Hom-Lie algebra.</p></abstract>

APA, Harvard, Vancouver, ISO, and other styles

40

Walendziak, Andrzej. "Deductive systems of pseudo-M algebras." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 21, no. 1 (January 1, 2022): 93–116. http://dx.doi.org/10.2478/aupcsm-2022-0008.

Full text

Abstract:

Abstract The class of pseudo-M algebras contains pseudo-BCK, pseudo-BCI, pseudo-BCH, pseudo-BE, pseudo-CI algebras and many other algebras of logic. In this paper, the notion of deductive system in a pseudo-M algebra is introduced and its elementary properties are investigated. Closed deductive systems are defined and studied. The homomorphic properties of (closed) deductive systems are provided. The concepts of translation deductive systems and R-congruences in pseudo-M algebras are introduced and investigated. It is shown that there is a bijection between closed translation deductive systems and R-congruences. Finally, the construction of quotient algebra 𝒜/D of a pseudo-M algebra 𝒜 via a translation deductive system D of 𝒜 is given.

APA, Harvard, Vancouver, ISO, and other styles

41

Sahami, Amir, Mehdi Rostami, Seyedeh Fatemeh Shariati, and Salman Babayi. "On Some Homological Properties of Hypergroup Algebras with Relation to Their Character Spaces." Journal of Mathematics 2022 (January 29, 2022): 1–5. http://dx.doi.org/10.1155/2022/4939971.

Full text

Abstract:

In this paper, we study the notion of approximate biprojectivity and left φ -biprojectivity of some Banach algebras, where φ is a character. Indeed, we show that approximate biprojectivity of the hypergroup algebra L 1 K implies that K is compact. Moreover, we investigate left φ -biprojectivity of certain hypergroup algebras, namely, abstract Segal algebras. As a main result, we conclude that (with some mild conditions) the abstract Segal algebra B is left φ -biprojective if and only if K is compact, where K is a hypergroup. We also study the approximate biflatness and left φ -biflatness of hypergroup algebras in terms of amenability of their related hypergroups.

APA, Harvard, Vancouver, ISO, and other styles

42

Cadavid, Paula, Mary Luz Rodiño Montoya, and Pablo M. Rodriguez. "The connection between evolution algebras, random walks and graphs." Journal of Algebra and Its Applications 19, no. 02 (January 29, 2019): 2050023. http://dx.doi.org/10.1142/s0219498820500231.

Full text

Abstract:

Evolution algebras are a new type of non-associative algebras which are inspired from biological phenomena. A special class of such algebras, called Markov evolution algebras, is strongly related to the theory of discrete time Markov chains. The winning of this relation is that many results coming from Probability Theory may be stated in the context of Abstract Algebra. In this paper, we explore the connection between evolution algebras, random walks and graphs. More precisely, we study the relationships between the evolution algebra induced by a random walk on a graph and the evolution algebra determined by the same graph. Given that any Markov chain may be seen as a random walk on a graph, we believe that our results may add a new landscape in the study of Markov evolution algebras.

APA, Harvard, Vancouver, ISO, and other styles

43

Pelaitay, Gustavo, and Maia Starobinsky. "A topological duality for tense modal pseudocomplemented De Morgan algebras." Mathematica Slovaca 74, no. 3 (June 1, 2024): 543–62. http://dx.doi.org/10.1515/ms-2024-0041.

Full text

Abstract:

Abstract In this paper, we define and study the variety of tense modal pseudocomplemented De Morgan algebras. This variety is a proper subvariety of the variety of tense tetravalent modal algebras. A tense modal pseudocomplemented De Morgan algebra is a modal pseudocomplemented De Morgan algebra endowed with two tense operators G and H satisfying additional conditions. Also, the variety of tense modal pseudocomplemented De Morgan algebras is intimately connected with some well-known varieties of De Morgan algebras with tense operators.

APA, Harvard, Vancouver, ISO, and other styles

44

Berenstein, Arkady, and Karl Schmidt. "Factorizable Module Algebras." International Mathematics Research Notices 2019, no. 21 (February 1, 2018): 6711–64. http://dx.doi.org/10.1093/imrn/rnx307.

Full text

Abstract:

Abstract The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras that we call factorizable by generalizing the Gauss factorization of square or rectangular matrices. This class includes coordinate algebras of corresponding reductive groups G, their parabolic subgroups, basic affine spaces, and many others. It turns out that products of factorizable algebras are also factorizable and it is easy to create a factorizable algebra out of virtually any $\mathfrak{g}$-module algebra. We also have quantum versions of all these constructions in the category of $U_{q}(\mathfrak{g})$-module algebras. Quite surprisingly, our quantum factorizable algebras are naturally acted on by the quantized enveloping algebra $U_{q}(\mathfrak{g}^{\ast })$ of the dual Lie bialgebra $\mathfrak{g}^{\ast }$ of $\mathfrak{g}$.

APA, Harvard, Vancouver, ISO, and other styles

45

Hussain, Naveed, Stephen S. T. Yau, and Huaiqing Zuo. "Geometric nilpotent Lie algebras and zero-dimensional simple complete intersection singularities." Forum Mathematicum 34, no. 2 (January 6, 2022): 323–45. http://dx.doi.org/10.1515/forum-2021-0227.

Full text

Abstract:

Abstract The Levi theorem tells us that every finite-dimensional Lie algebra is the semi-direct product of a semi-simple Lie algebra and a solvable Lie algebra. Brieskorn gave the connection between simple Lie algebras and simple singularities. Simple Lie algebras have been well understood, but not the solvable (nilpotent) Lie algebras. Therefore, it is important to establish connections between singularities and solvable (nilpotent) Lie algebras. In this paper, we give a new connection between nilpotent Lie algebras and nilradicals of derivation Lie algebras of isolated complete intersection singularities. As an application, we obtain the correspondence between the nilpotent Lie algebras of dimension less than or equal to 7 and the nilradicals of derivation Lie algebras of isolated complete intersection singularities with modality less than or equal to 1. Moreover, we give a new characterization theorem for zero-dimensional simple complete intersection singularities.

APA, Harvard, Vancouver, ISO, and other styles

46

Givant, Steven, and Hajnal Andréka. "Groups and Algebras of Binary Relations." Bulletin of Symbolic Logic 8, no. 1 (March 2002): 38–64. http://dx.doi.org/10.2178/bsl/1182353852.

Full text

Abstract:

AbstractIn 1941, Tarski published an abstract, finitely axiomatized version of the theory of binary relations, called the theory of relation algebras. He asked whether every model of his abstract theory could be represented as a concrete algebra of binary relations. He and Jónsson obtained some initial, positive results for special classes of abstract relation algebras. But Lyndon showed, in 1950, that in general the answer to Tarski's question is negative. Monk proved later that the answer remains negative even if one adjoins finitely many new axioms to Tarski's system. In this paper we describe a far-reaching generalization of the positive results of Jónsson and Tarski, as well as of some later, related results of Maddux. We construct a class of concrete models of Tarski's axioms—called coset relation algebras—that are very close in spirit to algebras of binary relations, but are built using systems of groups and cosets instead of elements of a base set. The models include all algebras of binary relations, and many non-representable relation algebras as well. We prove that every atomic relation algebra satisfying a certain measurability condition—a condition generalizing the conditions imposed by Jónsson and Tarski—is essentially isomorphic to a coset relation algebra. The theorem raises the possibility of providing a positive solution to Tarski's problem by using coset relation algebras instead of the standard algebras of binary relations.

APA, Harvard, Vancouver, ISO, and other styles

47

Lord, Nick, and Karlheintz Spindler. "Abstract Algebra with Applications." Mathematical Gazette 79, no. 486 (November 1995): 618. http://dx.doi.org/10.2307/3618116.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Woodgate, Brian, and Carol Whitehead. "Guide to Abstract Algebra." Mathematical Gazette 73, no. 465 (October 1989): 256. http://dx.doi.org/10.2307/3618479.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Mackiw, George. "Computing in Abstract Algebra." College Mathematics Journal 27, no. 2 (March 1996): 136. http://dx.doi.org/10.2307/2687404.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Baylis, John, and W. Keith Nicholson. "Introduction to Abstract Algebra." Mathematical Gazette 84, no. 499 (March 2000): 177. http://dx.doi.org/10.2307/3621549.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!