Log in

Relevant bibliographies by topics / Abelian category / Journal articles

To see the other types of publications on this topic, follow the link: Abelian category.

Journal articles on the topic 'Abelian category'

Author: Grafiati

Published: 4 June 2021

Last updated: 20 February 2023

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 'Abelian category.'

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

Song, Keyan, Liusan Wu, and Yuehui Zhang. "Endomorphism category of an abelian category." Communications in Algebra 46, no. 7 (December 15, 2017): 3062–70. http://dx.doi.org/10.1080/00927872.2017.1404072.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Vanderpool, Ruth. "Category ofp-Complete Abelian Groups." Communications in Algebra 40, no. 8 (August 2012): 2949–61. http://dx.doi.org/10.1080/00927872.2011.587856.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Rasuli, R. "Serre subcategory in Abelian category." International Journal of Algebra 7 (2013): 549–57. http://dx.doi.org/10.12988/ija.2013.3548.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Rudakov, Alexei. "Stability for an Abelian Category." Journal of Algebra 197, no. 1 (November 1997): 231–45. http://dx.doi.org/10.1006/jabr.1997.7093.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Abdelalim, S., and H. Essannouni. "Characterization of the automorphisms having the lifting property in the category of abelianp-groups." International Journal of Mathematics and Mathematical Sciences 2003, no. 71 (2003): 4511–16. http://dx.doi.org/10.1155/s016117120321067x.

Full text

Abstract:

Letpbe a prime. It is shown that an automorphismαof an abelianp-groupAlifts to any abelianp-group of whichAis a homomorphic image if and only ifα=π idA, withπan invertiblep-adic integer. It is also shown that ifAis torsion group or torsion-freep-divisible group, thenidAand−idAare the only automorphisms ofAwhich possess the lifting property in the category of abelian groups.

APA, Harvard, Vancouver, ISO, and other styles

6

Pajoohesh, Homeira. "A relationship between the category of chain MV-algebras and a subcategory of abelian groups." Mathematica Slovaca 71, no. 4 (August 1, 2021): 1027–45. http://dx.doi.org/10.1515/ms-2021-0037.

Full text

Abstract:

Abstract The category of MV-algebras is equivalent to the category of abelian lattice ordered groups with strong units. In this article we introduce the category of circled abelian groups and prove that the category of chain MV-algebras is isomorphic with the category of chain circled abelian groups. In the last section we show that the category of chain MV-algebras is a subcategory of abelian cyclically ordered groups.

APA, Harvard, Vancouver, ISO, and other styles

7

Albrecht, Ulrich F. "Extension functors on the category of $A$-solvable abelian groups." Czechoslovak Mathematical Journal 41, no. 4 (1991): 685–94. http://dx.doi.org/10.21136/cmj.1991.102499.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Arapura, Donu. "An abelian category of motivic sheaves." Advances in Mathematics 233, no. 1 (January 2013): 135–95. http://dx.doi.org/10.1016/j.aim.2012.10.004.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Sherman, C. "On K1 of an Abelian Category." Journal of Algebra 163, no. 2 (January 1994): 568–82. http://dx.doi.org/10.1006/jabr.1994.1032.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Barbieri-Viale, Luca, and Bruno Kahn. "A universal rigid abelian tensor category." Documenta Mathematica 27 (2022): 699–717. http://dx.doi.org/10.4171/dm/882.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Yu, Chia-Fu. "Abelian varieties over finite fields as basic abelian varieties." Forum Mathematicum 29, no. 2 (March 1, 2017): 489–500. http://dx.doi.org/10.1515/forum-2014-0141.

Full text

Abstract:

AbstractIn this note we show that any basic abelian variety with additional structures over an arbitrary algebraically closed field of characteristic ${p>0}$ is isogenous to another one defined over a finite field. We also show that the category of abelian varieties over finite fields up to isogeny can be embedded into the category of basic abelian varieties with suitable endomorphism structures. Using this connection, we derive a new mass formula for a finite orbit of polarized abelian surfaces over a finite field.

APA, Harvard, Vancouver, ISO, and other styles

12

RICKARD, JEREMY. "A COCOMPLETE BUT NOT COMPLETE ABELIAN CATEGORY." Bulletin of the Australian Mathematical Society 101, no. 3 (February 5, 2020): 442–45. http://dx.doi.org/10.1017/s0004972719001333.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Ardizzoni, Alessandro. "The category of modules over a monoidal category: Abelian or not?" ANNALI DELL UNIVERSITA DI FERRARA 50, no. 1 (December 2004): 167–85. http://dx.doi.org/10.1007/bf02825349.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Rump, Wolfgang. "The abelian closure of an exact category." Journal of Pure and Applied Algebra 224, no. 10 (October 2020): 106395. http://dx.doi.org/10.1016/j.jpaa.2020.106395.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Liu, Yu, and Panyue Zhou. "Abelian categories arising from cluster tilting subcategories II: quotient functors." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 6 (July 19, 2019): 2721–56. http://dx.doi.org/10.1017/prm.2019.42.

Full text

Abstract:

AbstractIn this paper, we consider a kind of ideal quotient of an extriangulated category such that the ideal is the kernel of a functor from this extriangulated category to an abelian category. We study a condition when the functor is dense and full, in another word, the ideal quotient becomes abelian. Moreover, a new equivalent characterization of cluster tilting subcategories is given by applying homological methods according to this functor. As an application, we show that in a connected 2-Calabi-Yau triangulated category ℬ, a functorially finite, extension closed subcategory 𝒯 of ℬ is cluster tilting if and only if ℬ /𝒯 is an abelian category.

APA, Harvard, Vancouver, ISO, and other styles

16

ZHENG, QILIAN, and JIAQUN WEI. "QUOTIENT CATEGORIES OF n-ABELIAN CATEGORIES." Glasgow Mathematical Journal 62, no. 3 (September 30, 2019): 673–705. http://dx.doi.org/10.1017/s0017089519000417.

Full text

Abstract:

AbstractThe notion of mutation pairs of subcategories in an n-abelian category is defined in this paper. Let ${\cal D} \subseteq {\cal Z}$ be subcategories of an n-abelian category ${\cal A}$. Then the quotient category ${\cal Z}/{\cal D}$ carries naturally an (n + 2) -angulated structure whenever $ ({\cal Z},{\cal Z}) $ forms a ${\cal D} \subseteq {\cal Z}$-mutation pair and ${\cal Z}$ is extension-closed. Moreover, we introduce strongly functorially finite subcategories of n-abelian categories and show that the corresponding quotient categories are one-sided (n + 2)-angulated categories. Finally, we study homological finiteness of subcategories in a mutation pair.

APA, Harvard, Vancouver, ISO, and other styles

17

Lo, Jason. "Torsion pairs and filtrations in abelian categories with tilting objects." Journal of Algebra and Its Applications 14, no. 08 (April 27, 2015): 1550121. http://dx.doi.org/10.1142/s0219498815501212.

Full text

Abstract:

Given a noetherian abelian k-category [Formula: see text] of finite homological dimension, with a tilting object T of projective dimension 2, the abelian category [Formula: see text] and the abelian category of modules over End (T) op are related by a sequence of two tilts; we give an explicit description of the torsion pairs involved. We then use our techniques to obtain a simplified proof of a theorem of Jensen–Madsen–Su, that [Formula: see text] has a three-step filtration by extension-closed subcategories. Finally, we generalize Jensen–Madsen–Su's filtration to the case where T has any finite projective dimension.

APA, Harvard, Vancouver, ISO, and other styles

18

Elfiyanti, Gustina, Intan Muchtadi-Alamsyah, Fajar Yuliawan, and Dellavitha Nasution. "On the Category of Weakly U-Complexes." European Journal of Pure and Applied Mathematics 13, no. 2 (April 29, 2020): 323–45. http://dx.doi.org/10.29020/nybg.ejpam.v13i2.3673.

Full text

Abstract:

Motivated by a study of Davvaz and Shabbani which introduced the concept of U-complexes and proposed a generalization on some results in homological algebra, we study thecategory of U-complexes and the homotopy category of U-complexes. In [8] we said that the category of U-complexes is an abelian category. Here, we show that the object that we claimed to be the kernel of a morphism of U-omplexes does not satisfy the universal property of the kernel, hence wecan not conclude that the category of U-complexes is an abelian category. The homotopy category of U-complexes is an additive category. In this paper, we propose a weakly chain U-complex by changing the second condition of the chain U-complex. We prove that the homotopy category ofweakly U-complexes is a triangulated category.

APA, Harvard, Vancouver, ISO, and other styles

19

Kong, Fan. "Characterizing When the Category of Gorenstein Projective Modules is an Abelian Category." Algebras and Representation Theory 17, no. 4 (August 25, 2013): 1289–301. http://dx.doi.org/10.1007/s10468-013-9448-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Posur, Sebastian. "Closing the category of finitely presented functors under images made constructive." Compositionality 2 (September 1, 2020): 4. http://dx.doi.org/10.32408/compositionality-2-4.

Full text

Abstract:

For an additive category P we provide an explicit construction of a category Q(P) whose objects can be thought of as formally representing im(γ)im(ρ)∩im(γ) for given morphisms γ:A→B and ρ:C→B in P, even though P does not need to admit quotients or images. We show how it is possible to calculate effectively within Q(P), provided that a basic problem related to syzygies can be handled algorithmically. We prove an equivalence of Q(P) with the smallest subcategory of the category of contravariant functors from P to the category of abelian groups Ab which contains all finitely presented functors and is closed under the operation of taking images. Moreover, we characterize the abelian case: Q(P) is abelian if and only if it is equivalent to fp(Pop,Ab), the category of all finitely presented functors, which in turn, by a theorem of Freyd, is abelian if and only if P has weak kernels.The category Q(P) is a categorical abstraction of the data structure for finitely presented R-modules employed by the computer algebra system Macaulay2, where R is a ring. By our generalization to arbitrary additive categories, we show how this data structure can also be used for modeling finitely presented graded modules, finitely presented functors, and some not necessarily finitely presented modules over a non-coherent ring.

APA, Harvard, Vancouver, ISO, and other styles

21

Kiep̵iński, Roman. "A characterization of rings over which abelian Hopf algebras form an abelian category." Journal of Pure and Applied Algebra 52, no. 1-2 (May 1988): 59–76. http://dx.doi.org/10.1016/0022-4049(88)90135-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

Chen, Qinghua, and Min Zheng. "K-Groups of Trivial Extensions and Gluings of Abelian Categories." Mathematics 9, no. 16 (August 6, 2021): 1864. http://dx.doi.org/10.3390/math9161864.

Full text

Abstract:

This paper focuses on the Ki-groups of two types of extensions of abelian categories, which are the trivial extension and the gluing of abelian categories. We prove that, under some conditions, Ki-groups of a certian subcategory of the trivial extension category is isomorphic to Ki-groups of the similar subcategory of the original category. Moreover, under some conditions, we show that the Ki-groups of a left (right) gluing of two abelian categories are isomorphic to the direct sum of Ki-groups of two abelian categories. As their applications, we obtain some results of the Ki-groups of the trivial extension of a ring by a bimodule (i∈N).

APA, Harvard, Vancouver, ISO, and other styles

23

García, J., and J. Martínez Hernández. "When is the category of flat modules abelian?" Fundamenta Mathematicae 147, no. 1 (1995): 83–91. http://dx.doi.org/10.4064/fm-147-1-83-91.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Aghapournahr, Moharram. "Abelian Category of Cominimax and Weakly Cofinite Modules." Taiwanese Journal of Mathematics 20, no. 5 (September 2016): 1001–8. http://dx.doi.org/10.11650/tjm.20.2016.7324.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Timoshenko, E. A. "T-radicals in the category of Abelian groups." Journal of Mathematical Sciences 154, no. 3 (October 2008): 411–21. http://dx.doi.org/10.1007/s10958-008-9171-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Elfiyanti, Gustina, Intan Muchtadi-Alamsyah, Dellavitha Nasution, and Utih Amartiwi. "Abelian property of the category of U-complexes." International Journal of Mathematical Analysis 10 (2016): 849–53. http://dx.doi.org/10.12988/ijma.2016.6682.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Kalebogaz, Berke, and Derya Keskin Tütüncü. "(D4)-Objects in Abelian Categories." Algebra Colloquium 29, no. 02 (April 30, 2022): 231–40. http://dx.doi.org/10.1142/s1005386722000190.

Full text

Abstract:

Let 𝒜 be an abelian category and [Formula: see text]. Then M is called a [Formula: see text]-object if, whenever A and B are subobjects of M with [Formula: see text] and [Formula: see text] is an epimorphism, [Formula: see text] is a direct summand of A. In this paper we give several equivalent conditions of [Formula: see text]-objects in an abelian category. Among other results, we prove that any object M in an abelian category 𝒜 is [Formula: see text] if and only if for every subobject K of M such that K is the intersection [Formula: see text] of perspective direct summands [Formula: see text] and [Formula: see text] of M with [Formula: see text], every morphismr [Formula: see text] can be lifted to an endomorphism [Formula: see text] in [Formula: see text].

APA, Harvard, Vancouver, ISO, and other styles

28

Angiono, Iván, and César Galindo. "Pointed finite tensor categories over abelian groups." International Journal of Mathematics 28, no. 11 (October 2017): 1750087. http://dx.doi.org/10.1142/s0129167x17500872.

Full text

Abstract:

We give a characterization of finite pointed tensor categories obtained as de-equivariantizations of the category of corepresentations of finite-dimensional pointed Hopf algebras with abelian group of group-like elements only in terms of the (cohomology class of the) associator of the pointed part. As an application we prove that every coradically graded pointed finite braided tensor category is a de-equivariantization of the category of corepresentations of a finite-dimensional pointed Hopf algebras with abelian group of group-like elements.

APA, Harvard, Vancouver, ISO, and other styles

29

LI, HAISHENG. "ON ABELIAN COSET GENERALIZED VERTEX ALGEBRAS." Communications in Contemporary Mathematics 03, no. 02 (May 2001): 287–340. http://dx.doi.org/10.1142/s0219199701000366.

Full text

Abstract:

This paper studies the algebraic aspect of a general abelian coset theory with a work of Dong and Lepowsky as our main motivation. It is proved that the vacuum space ΩV (or the space of highest weight vectors) of a Heisenberg algebra in a general vertex operator algebra V has a natural generalized vertex algebra structure in the sense of Dong and Lepowsky and that the vacuum space ΩW of a V-module W is a natural ΩV-module. The automorphism group Aut ΩVΩV of the adjoint ΩV-module is studied and it is proved to be a central extension of a certain torsion free abelian group by C×. For certain subgroups A of Aut ΩVΩV, certain quotient algebras [Formula: see text] of ΩV are constructed. Furthermore, certain functors among the category of V-modules, the category of ΩV-modules and the category of [Formula: see text]-modules are constructed and irreducible ΩV-modules and [Formula: see text]-modules are classified in terms of irreducible V-modules. If the category of V-modules is semisimple, then it is proved that the category of [Formula: see text]-modules is semisimple.

APA, Harvard, Vancouver, ISO, and other styles

30

Lyubashenko, V. "Ribbon Abelian Categories as Modular Categories." Journal of Knot Theory and Its Ramifications 05, no. 03 (June 1996): 311–403. http://dx.doi.org/10.1142/s0218216596000229.

Full text

Abstract:

A category N of labeled (oriented) trivalent graphs (nets) or ribbon graphs is extended by new generators called fusing, braiding, twist and switch with relations which can be called Moore-Seiberg relations. A functor to N is constructed from the category Surf of oriented surfaces with labeled boundary and their homeomorphisms. Given a (eventually non-semisimple) k-linear abelian ribbon braided category [Formula: see text] with some finiteness conditions we construct a functor from a central extension of N with the set of labels [Formula: see text] ObC to k-vector spaces. Composing the functors we get a modular functor from a central extension of Surfto k-vector spaces.

APA, Harvard, Vancouver, ISO, and other styles

31

BARAKAT, MOHAMED, and MARKUS LANGE-HEGERMANN. "AN AXIOMATIC SETUP FOR ALGORITHMIC HOMOLOGICAL ALGEBRA AND AN ALTERNATIVE APPROACH TO LOCALIZATION." Journal of Algebra and Its Applications 10, no. 02 (April 2011): 269–93. http://dx.doi.org/10.1142/s0219498811004562.

Full text

Abstract:

In this paper we develop an axiomatic setup for algorithmic homological algebra of Abelian categories. This is done by exhibiting all existential quantifiers entering the definition of an Abelian category, which for the sake of computability need to be turned into constructive ones. We do this explicitly for the often-studied example Abelian category of finitely presented modules over a so-called computable ring R, i.e. a ring with an explicit algorithm to solve one-sided (in)homogeneous linear systems over R. For a finitely generated maximal ideal 𝔪 in a commutative ring R, we show how solving (in)homogeneous linear systems over R𝔪 can be reduced to solving associated systems over R. Hence, the computability of R implies that of R𝔪. As a corollary, we obtain the computability of the category of finitely presented R𝔪-modules as an Abelian category, without the need of a Mora-like algorithm. The reduction also yields, as a byproduct, a complexity estimation for the ideal membership problem over local polynomial rings. Finally, in the case of localized polynomial rings, we demonstrate the computational advantage of our homologically motivated alternative approach in comparison to an existing implementation of Mora's algorithm.

APA, Harvard, Vancouver, ISO, and other styles

32

Huybrechts, Daniel, Emanuele Macrì, and Paolo Stellari. "Stability conditions for generic K3 categories." Compositio Mathematica 144, no. 1 (January 2008): 134–62. http://dx.doi.org/10.1112/s0010437x07003065.

Full text

Abstract:

AbstractA K3 category is by definition a Calabi–Yau category of dimension two. Geometrically K3 categories occur as bounded derived categories of (twisted) coherent sheaves on K3 or abelian surfaces. A K3 category is generic if there are no spherical objects (or just one up to shift). We study stability conditions on K3 categories as introduced by Bridgeland and prove his conjecture about the topology of the stability manifold and the autoequivalences group for generic twisted projective K3, abelian surfaces, and K3 surfaces with trivial Picard group.

APA, Harvard, Vancouver, ISO, and other styles

33

BARNES, DAVID. "A monoidal algebraic model for rational SO(2)-spectra." Mathematical Proceedings of the Cambridge Philosophical Society 161, no. 1 (April 11, 2016): 167–92. http://dx.doi.org/10.1017/s0305004116000219.

Full text

Abstract:

AbstractThe category of rational SO(2)–equivariant spectra admits an algebraic model. That is, there is an abelian category ${\mathcal A}$(SO(2)) whose derived category is equivalent to the homotopy category of rational SO(2)–equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra?The category ${\mathcal A}$(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non–Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on ${\mathcal A}$(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K(p)–local stable homotopy category.A monoidal Quillen equivalence to a simpler monoidal model category R•-mod that has explicit generating sets is also given. Having monoidal model structures on ${\mathcal A}$(SO(2)) and R•-mod removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)–equivariant spectra.

APA, Harvard, Vancouver, ISO, and other styles

34

Cherlin, Gregory, and Adrien Deloro. "Small representations of SL2 in the finite Morley rank category." Journal of Symbolic Logic 77, no. 3 (September 2012): 919–33. http://dx.doi.org/10.2178/jsl/1344862167.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

GONZÁLEZ-FÉREZ, JUAN, and LEANDRO MARÍN. "MONOMORPHISMS AND KERNELS IN THE CATEGORY OF FIRM MODULES." Glasgow Mathematical Journal 52, A (June 24, 2010): 83–91. http://dx.doi.org/10.1017/s0017089510000224.

Full text

Abstract:

AbstractIn this paper we consider for a non-unital ring R, the category of firm R-modules for a non-unital ring R, i.e. the modules M such that the canonical morphism μM : R ⊗RM → M given by r ⊗ m ↦ rm is an isomorphism. This category is a natural generalization of the usual category of unitary modules for a ring with identity and shares many properties with it. The only difference is that monomorphisms are not always kernels. It has been proved recently that this category is not Abelian in general by providing an example of a monomorphism that is not a kernel in a particular case. In this paper we study the lattices of monomorphisms and kernels, proving that the lattice of monomorphisms is a modular lattice and that the category of firm modules is Abelian if and only if the composition of two kernels is a kernel.

APA, Harvard, Vancouver, ISO, and other styles

36

Khusainov, A. A. "On extension groups in the category of Abelian diagrams." Siberian Mathematical Journal 33, no. 1 (1992): 149–54. http://dx.doi.org/10.1007/bf00972947.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Proskurin, N. V. "Zeta Function of the Category of Finite Abelian Groups." Journal of Mathematical Sciences 225, no. 6 (August 12, 2017): 991–93. http://dx.doi.org/10.1007/s10958-017-3510-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Bahmanpour, Kamal, Reza Naghipour, and Monireh Sedghi. "On the category of cofinite modules which is Abelian." Proceedings of the American Mathematical Society 142, no. 4 (January 6, 2014): 1101–7. http://dx.doi.org/10.1090/s0002-9939-2014-11836-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

González-Férez, Juan, and Leandro Marín. "The category of firm modules need not be abelian." Journal of Algebra 318, no. 1 (December 2007): 377–92. http://dx.doi.org/10.1016/j.jalgebra.2007.08.007.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Kawasaki, Ken-ichiroh. "On a category of cofinite modules which is Abelian." Mathematische Zeitschrift 269, no. 1-2 (July 15, 2010): 587–608. http://dx.doi.org/10.1007/s00209-010-0751-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Estrada, Sergio, and James Gillespie. "The projective stable category of a coherent scheme." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 1 (February 26, 2018): 15–43. http://dx.doi.org/10.1017/s0308210517000385.

Full text

Abstract:

We define the projective stable category of a coherent scheme. It is the homotopy category of an abelian model structure on the category of unbounded chain complexes of quasi-coherent sheaves. We study the cofibrant objects of this model structure, which are certain complexes of flat quasi-coherent sheaves satisfying a special acyclicity condition.

APA, Harvard, Vancouver, ISO, and other styles

42

Khusainov, A. A. "On the global dimension of the category of commutative diagrams in an abelian category." Siberian Mathematical Journal 37, no. 5 (September 1996): 1041–51. http://dx.doi.org/10.1007/bf02110735.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Backelin, Erik, and Omar Jaramillo. "Auslander–Reiten sequences and t-structures on the homotopy category of an abelian category." Journal of Algebra 339, no. 1 (August 2011): 80–96. http://dx.doi.org/10.1016/j.jalgebra.2011.04.037.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

FATICONI, THEODORE G. "DIAGRAMS OF AN ABELIAN GROUP." Bulletin of the Australian Mathematical Society 80, no. 1 (July 6, 2009): 38–64. http://dx.doi.org/10.1017/s0004972708001238.

Full text

Abstract:

AbstractIn this paper, we characterize quadratic number fields possessing unique factorization in terms of the power cancellation property of torsion-free rank-two abelian groups, in terms of Σ-unique decomposition, in terms of a pair of point set topological properties of Eilenberg–Mac Lane spaces, and in terms of the sequence of rational primes. We give a complete set of topological invariants of abelian groups, we characterize those abelian groups that have the power cancellation property in the category of abelian groups, and we characterize those abelian groups that have Σ-unique decomposition. Our methods can be used to characterize any direct sum decomposition property of an abelian group.

APA, Harvard, Vancouver, ISO, and other styles

45

Bahmanpour, Kamal. "On the Category of Weakly Laskerian Cofinite Modules." MATHEMATICA SCANDINAVICA 115, no. 1 (August 12, 2014): 62. http://dx.doi.org/10.7146/math.scand.a-18002.

Full text

Abstract:

Let $R$ denote a commutative Noetherian (not necessarily local) ring and $I$ be an ideal of $R$. The main purpose of this note is to show that the category $\mathscr{WL}(R, I)_{\it cof}$ of $I$-cofinite weakly Laskerian $R$-modules forms an Abelian subcategory of the category of all $R$-modules.

APA, Harvard, Vancouver, ISO, and other styles

46

Enochs, Edgar, J. R. García Rozas, Luis Oyonarte, and Overtoun M. G. Jenda. "Conormal morphisms." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 133, no. 5 (October 2003): 1047–56. http://dx.doi.org/10.1017/s0308210500002808.

Full text

Abstract:

This article represents another step in our programme of obtaining a Galois theory and a coGalois theory when we have a category C and a given enveloping (for Galois) or covering (for coGalois) class. More precisely, in this paper, we study what should be understood by a conormal morphism between two objects of a given category and we characterize conormal morphisms between finite abelian groups when the covering class under consideration is that of torsion-free abelian groups.

APA, Harvard, Vancouver, ISO, and other styles

47

Yang, Xiaoyan, and Tianya Cao. "Cotorsion Pairs in 𝒞N(A)." Algebra Colloquium 24, no. 04 (November 15, 2017): 577–602. http://dx.doi.org/10.1142/s1005386717000384.

Full text

Abstract:

Given a cotorsion pair ([Formula: see text], [Formula: see text]) in an abelian category [Formula: see text] , we define cotorsion pairs ([Formula: see text], dg[Formula: see text]) and (dg[Formula: see text], [Formula: see text]) in the category [Formula: see text]N([Formula: see text]) of N-complexes on [Formula: see text]. We prove that if the cotorsion pair ([Formula: see text], [Formula: see text]) is complete and hereditary in a bicomplete abelian category, then both of the induced cotorsion pairs are complete, compatible and hereditary. We also create complete cotorsion pairs (dw[Formula: see text], (dw[Formula: see text])⊥), (ex[Formula: see text], (ex[Formula: see text])⊥) and (⊥(dw[Formula: see text]), dw[Formula: see text]), (⊥(ex[Formula: see text]); ex[Formula: see text]) in a termwise manner by starting with a cotorsion pair ([Formula: see text], [Formula: see text]) that is cogenerated by a set. As applications of these results, we obtain more abelian model structures from the cotorsion pairs.

APA, Harvard, Vancouver, ISO, and other styles

48

Banerjee, Abhishek. "On Auslander’s formula and cohereditary torsion pairs." Communications in Contemporary Mathematics 20, no. 06 (August 27, 2018): 1750071. http://dx.doi.org/10.1142/s0219199717500717.

Full text

Abstract:

For a small abelian category [Formula: see text], Auslander’s formula allows us to express [Formula: see text] as a quotient of the category [Formula: see text] of coherent functors on [Formula: see text]. We consider an abelian category with the added structure of a cohereditary torsion pair [Formula: see text]. We prove versions of Auslander’s formula for the torsion-free class [Formula: see text] of [Formula: see text], for the derived torsion-free class [Formula: see text] of the triangulated category [Formula: see text] as well as the induced torsion-free class in the ind-category [Formula: see text] of [Formula: see text]. Further, for a given regular cardinal [Formula: see text], we also consider the category [Formula: see text] of [Formula: see text]-presentable objects in the functor category [Formula: see text]. Then, under certain conditions, we show that the torsion-free class [Formula: see text] can be recovered as a subquotient of [Formula: see text].

APA, Harvard, Vancouver, ISO, and other styles

49

Sharma, Poonam Kumar, Chandni, and Nitin Bhardwaj. "Category of Intuitionistic Fuzzy Modules." Mathematics 10, no. 3 (January 27, 2022): 399. http://dx.doi.org/10.3390/math10030399.

Full text

Abstract:

We study the relationship between the category of R-modules (CR-M) and the category of intuitionistic fuzzy modules (CR−IFM). We construct a category CLat(R−IFM) of complete lattices corresponding to every object in CR−M and then show that, corresponding to each morphism in CR−M, there exists a contravariant functor from CR−IFM to the category CLat (=union of all CLat(R−IFM), corresponding to each object in CR−M) that preserve infima. Then, we show that the category CR−IFM forms a top category over the category CR−M. Finally, we define and discuss the concept of kernel and cokernel in CR−IFM and show that CR−IFM is not an Abelian Category.

APA, Harvard, Vancouver, ISO, and other styles

50

Patashnick, Owen. "A Candidate for the Abelian Category of Mixed Elliptic Motives." Journal of K-theory 12, no. 3 (November 15, 2013): 569–600. http://dx.doi.org/10.1017/is013007012jkt237.

Full text

Abstract:

AbstractIn this work, we s uggest a defnition for the category of mixed motives generated by the motive h1 (E) for E an elliptic curve without complex multiplication. We then compute the cohomology of this category. Modulo a strengthening of the Beilinson-Soulé conjecture, we show that the cohomology of our category agrees with the expected motivic cohomology groups. Finally for each pure motive (Symnh1 (E)) (–1) we construct families of nontrivial motives whose highest associated weight graded piece is (Symnh1 (E)) (–1).

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!