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Journal articles on the topic 'Inner derivation'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Mohammed, N. F., Hanan F. Qasim, and Z. H. Maibed. "Outer derivations of low-dimensional diassociative algebras." Journal of Discrete Mathematical Sciences and Cryptography 28, no. 4-B (2025): 1369–73. https://doi.org/10.47974/jdmsc-2276.

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The work of outer derivations is extremely extensive research that occurs in many sorts of mathematics fields. This work is concerned with the description of outer derivation for diassociative algebras which is isomorphic to the first cohomology group. The inner derivation (resp. the derivation) interpreted as 1-coboundaries (resp. 1-cocycles). In this regard, we propose an algebraic method to get an important specific case of derivations, known as inner derivation. The procedure is used to determine the inner derivatives of diassociative algebras.

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2

Karimov, U. Sh. "Local derivations on real AW*-algebras." UZBEK MATHEMATICAL JOURNAL 68, no. 4 (2025): 96–99. https://doi.org/10.29229/uzmj.2024-4-10.

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In this article, we consider local derivations of real AW*-algebras. It has been proven that any derivation of real AW*-algebra whose complexification is (complex) AW*-algebra, is inner. Using a result by M. Bresar, we prove that any local derivation of a real AW*-algebra, whose enveloping algebra is a (complex) AW*-algebra, is a derivation. Consequently, any local derivation of a real W*- algebra is an inner derivation.

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3

Vladeva, Dimitrinka. "Derivations of polynomial semirings." International Journal of Algebra and Computation 30, no. 01 (2019): 1–12. http://dx.doi.org/10.1142/s0218196719500620.

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The aim of this paper is the investigation of derivations in semiring of polynomials over idempotent semiring. For semiring [Formula: see text], where [Formula: see text] is a commutative idempotent semiring we construct derivations corresponding to the polynomials from the principal ideal [Formula: see text] and prove that the set of these derivations is a non-commutative idempotent semiring closed under the Jordan product of derivations — Theorem 3.3. We introduce generalized inner derivations defined as derivations acting only over the coefficients of the polynomial and consider [Formula: s

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4

Mansuroğlu, Nil, and Mücahit Özkaya. "Almost inner derivations of Leibniz algebras." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 73, no. 4 (2024): 969–81. https://doi.org/10.31801/cfsuasmas.1485446.

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This work is presented the study on almost inner derivations of Leibniz algebras. In this note, we demonstrate the natural extensions of some general properties on derivations given for Lie algebras to Leibniz algebras with finite dimension, and also we investigate which statements a mapping have to hold to be an almost inner derivation.

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5

Luh, Jiang, and Youpei Ye. "Derivations of higher order in semiprime rings." International Journal of Mathematics and Mathematical Sciences 21, no. 1 (1998): 89–92. http://dx.doi.org/10.1155/s0161171298000106.

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LetRbe a2-torsion free semiprime ring with derivationd. Supposedd2nis a derivation ofR, wherenis a positive integer. It is shown that ifRis(4n−2)-torsion free or ifRis an inner derivation ofR, thend2n−1=0.

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6

Kaushik, Dr K. L. "Generalised Inner Derivations in Semi Prime Rings." International Journal of Innovative Science and Research Technology 5, no. 7 (2020): 372–74. http://dx.doi.org/10.38124/ijisrt20aug277.

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Let A be any ring and f(xy) = f(x)y+xha(y), where f be any generalised inner derivation(G.I.D ) a be the fixed element of A. In this paper, it is shown that (i) ha must necessarily be a derivation for semi prime ring A. (ii) ∃ no generalized inner derivations f : A → A such that f(x ◦ y) = x ◦ y or f(x ◦ y) + x ◦ y = 0 ∀ x,y ∈ A, We have proved Havala [2] def. p.1147, Herstein [3] Lemma 3.1 p. 1106 as corollaries, along with other results.

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7

Fošner, Ajda, and Tsiu-Kwen Lee. "Jordan *-Derivations of Finite-Dimensional Semiprime Algebras." Canadian Mathematical Bulletin 57, no. 1 (2014): 51–60. http://dx.doi.org/10.4153/cmb-2012-024-2.

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AbstractIn this paper, we characterize Jordan *-derivations of a 2-torsion free, finite-dimensional semiprime algebra R with involution *. To be precise, we prove the following. Let δ : R → R be a Jordan *-derivation. Then there exists a *-algebra decomposition R = U ⊕ V such that both U and V are invariant under δ. Moreover, * is the identity map of U and δ|U is a derivation, and the Jordan *-derivation δ|V is inner. We also prove the following. Let R be a noncommutative, centrally closed prime algebra with involution *, char R ≠ 2, and let δ be a nonzero Jordan *-derivation of R. If δ is an

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8

Erfanian, Attar, S. Barootkoob, and Vishki Ebrahimi. "On extension of bi-derivations to the bidual of Banach algebras." Filomat 30, no. 8 (2016): 2261–67. http://dx.doi.org/10.2298/fil1608261e.

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We present some necessary and sufficient conditions such that the (Arens) extensions of a bi-derivation on Banach algebras are again bi-derivations. We then examine our results for some Banach algebras. In particular, we show that the (Arens) extensions of a bi-derivation on C*-algebras are biderivations. Some results on extensions of an inner bi-derivation are also included.

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9

Patlertsin, Sutida, Suchada Pongprasert, and Thitarie Rungratgasame. "On Inner Derivations of Leibniz Algebras." Mathematics 12, no. 8 (2024): 1152. http://dx.doi.org/10.3390/math12081152.

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Leibniz algebras are generalizations of Lie algebras. Similar to Lie algebras, inner derivations play a crucial role in characterizing complete Leibniz algebras. In this work, we demonstrate that the algebra of inner derivations of a Leibniz algebra can be decomposed into the sum of the algebra of left multiplications and a certain ideal. Furthermore, we show that the quotient of the algebra of derivations of the Leibniz algebra by this ideal yields a complete Lie algebra. Our results independently establish that any derivation of a semisimple Leibniz algebra can be expressed as a combination

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10

Dadakhodjaev, R. A., and A. A. Rakhimov. "2-Local derivations of real AW*-algebras are derivation." Positivity 25, no. 4 (2021): 1351–56. http://dx.doi.org/10.1007/s11117-021-00815-8.

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Abstract2-Local derivations on real matrix algebras over unital semi-prime Banach algebras are considered. Using the real analogue of the result that any 2-local derivation on the algebra $$M_{2^n}(A)$$ M 2 n ( A ) ($$n\ge 2$$ n ≥ 2 ) is a derivation, it is shown that any 2-local derivation on real AW$$^*$$ ∗ -algebra for which the enveloping algebra is (complex) AW*-algebra, is a derivation, where A is a unital semi-prime Banach algebra with the inner derivation property.

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11

Li, Shan, Kaijia Luo, and Jiankui Li. "Generalized Lie $ n $-derivations on generalized matrix algebras." AIMS Mathematics 9, no. 10 (2024): 29386–403. http://dx.doi.org/10.3934/math.20241424.

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<p>Let $ \mathcal{G} $ be a generalized matrix algebra. We show that under certain conditions, each generalized Lie $ n $-derivation associated with a linear map on $ \mathcal{G} $ is a sum of a generalized derivation and a central map vanishing on all $ (n-1) $-th commutators and is also a sum of a generalized inner derivation and a Lie $ n $-derivation. As an application, generalized Lie $ n $-derivations on von Neumann algebras are characterized.</p>

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12

Didas, Michael, and Jörg Eschmeier. "Derivations on Toeplitz Algebras." Canadian Mathematical Bulletin 57, no. 2 (2014): 270–76. http://dx.doi.org/10.4153/cmb-2013-001-9.

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AbstractLet H2(Ω) be the Hardy space on a strictly pseudoconvex domain Ω ⊂ ℂn, and let A ⊂ L∞(∂Ω) denote the subalgebra of all L∞-functions ƒ with compact Hankel operator Hƒ. Given any closed subalgebra B ⊂ A containing C(Ω), we describe the first Hochschild cohomology group of the corresponding Toeplitz algebra 𝒯(B) ⊂ B(H2(Ω). In particular, we show that every derivation on 𝒯(A) is inner. These results are new even for n = 1, where it follows that every derivation on T(H∞ +C) is inner, while there are non-inner derivations on T(H∞ + C(∂ℝn)) over the unit ball Bn in dimension n > 1.

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13

Sun, Bing, Liangyun Chen, and Xin Zhou. "Double Derivations of n-Lie Superalgebras." Algebra Colloquium 25, no. 01 (2018): 161–80. http://dx.doi.org/10.1142/s1005386718000111.

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Let 𝔤 be an n-Lie superalgebra. We study the double derivation algebra [Formula: see text] and describe the relation between [Formula: see text] and the usual derivation Lie superalgebra Der(𝔤). We show that the set [Formula: see text] of all double derivations is a subalgebra of the general linear Lie superalgebra gl(𝔤) and the inner derivation algebra ad(𝔤) is an ideal of [Formula: see text]. We also show that if 𝔤 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad(𝔤) in [Formula: see text] is trivial. Finally, we give that for every perfec

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14

Arshad, Minahal, and M. Mobeen Munir. "On Lie Derivations, Generalized Lie Derivations and Lie Centralizers of Octonion Algebras." Ars Combinatoria 157 (December 31, 2023): 23–37. http://dx.doi.org/10.61091/ars157-02.

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Let L be a unital ring with characteristic different from 2 and O ( L ) be an algebra of Octonion over L . In the present article, our attempt is to present the characterization as well as the matrix representation of some variants of derivations on O ( L ) . The matrix representation of Lie derivation of O ( L ) and its decomposition in terms of Lie derivation and Jordan derivation of L and inner derivation of O is presented. The result about the decomposition of Lie centralizer of O in terms of Lie centralizer and Jordan centralizer of L is given. Moreover, the matrix representation of gener

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15

PAJOOHESH, H., P. RODRIGUEZ та C. WADDELL. "NILPOTENT INNER DERIVATIONS ON SOME SUBRINGS OF Mn(ℝ)". Journal of Algebra and Its Applications 12, № 08 (2013): 1350045. http://dx.doi.org/10.1142/s021949881350045x.

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It is known that the degree of nilpotency of a nilpotent derivation on a prime ring including the ring of n × n matrices must be an odd number. In this article we introduce subrings of the ring of of n × n matrices that admit derivations with an even degree of nilpotency.

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16

Mirzavaziri, Madjid, та Mohammad Sal Moslehian. "(σ, τ)-amenability of C*-algebras". gmj 18, № 1 (2011): 137–45. http://dx.doi.org/10.1515/gmj.2011.0013.

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Abstract Suppose that is an algebra, σ, τ : → are two linear mappings such that both σ() and τ() are subalgebras of and 𝒳 is a (τ(), σ())-bimodule. A linear mapping D : → 𝒳 is called a (σ, τ)-derivation if D(ab) = D(a) · σ(b) + τ(a) · D(b) (a, b ∈ ). A (σ, τ)-derivation D is called a (σ, τ)-inner derivation if there exists an x ∈ 𝒳 such that D is of the form either or . A Banach algebra is called (σ, τ)-amenable if every (σ, τ)-derivation from into a dual Banach (τ(), σ())-bimodule is (σ, τ)-inner. Studying some general algebraic aspects of (σ, τ)-derivations, we investigate the relation betwe

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17

Brešar, Matej, and Peter Šemrl. "Derivations mapping into the socle." Mathematical Proceedings of the Cambridge Philosophical Society 120, no. 2 (1996): 339–46. http://dx.doi.org/10.1017/s0305004100074892.

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Over the last few years a number of results giving conditions on a derivation of a Banach algebra implying that its range is contained in the radical have been obtained (see survey articles of Mathieu[7] and Murphy [8]). If an algebra is semi-simple, these conditions, of course, imply that a derivation is zero. In this paper we consider inner derivations that are non-zero in general, but their ranges are rather special and ‘small’ in some sense.

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18

Martín, A. J. Calderón, and M. Forero Piulestán. "Split Twisted Inner Derivation Triple Systems." Communications in Algebra 38, no. 1 (2009): 28–45. http://dx.doi.org/10.1080/00927870902829122.

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19

Jabbari, Ali, and Ali Ebadian. "Bi-derivations and quasi-multipliers on module extensions Banach algebras." Boletim da Sociedade Paranaense de Matemática 41 (December 26, 2022): 1–10. http://dx.doi.org/10.5269/bspm.52574.

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This paper characterize two bi-linear maps bi-derivations and quasi-multipliers on the module extension Banach algebra $A\oplus_1 X$, where $A$ is a Banach algebra and $X$ is a Banach $A$-module. Under some conditions, it is shown that if every bi-derivation on $A\oplus_1 A$ is inner, then the quotient group of bounded bi-derivations and inner bi-derivations, is equal to space of quasi-multipliers of $A$. Moreover, it is proved that $\mathrm{QM}(A \oplus_1 A)=\mathrm{QM}(A)\oplus (\mathrm{QM}(A)+\mathrm{QM}(A)')$, where $\mathrm{QM}(A)'=\{m\in \mathrm{QM}(A):m(0,a)=m(a,0)=0\}$.

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20

He, Hua, Xueyan Yang, and Zicong Yang. "Composition and Volterra-type inner derivations on the generalized Fock spaces." Filomat 38, no. 11 (2024): 3707–18. https://doi.org/10.2298/fil2411707h.

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A classical result of Calkin [3] says that the inner derivation maps the algebra of all bounded operators on a Hilbert space into the ideal of all compact operators if and only if the induced operator is a compact perturbation of the scalar operator. On the generalized Fock spaces, we use the compact intertwing relations to study the range of the inner derivations induced by the composition operators C? and the Volterra type operators Jg and Ig.

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21

SUZUKI, MASUO. "GENERAL FORMULATION OF QUANTUM ANALYSIS." Reviews in Mathematical Physics 11, no. 02 (1999): 243–65. http://dx.doi.org/10.1142/s0129055x9900009x.

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A general formulation of noncommutative or quantum derivatives for operators in a Banach space is given on the basis of the Leibniz rule, irrespective of their explicit representations such as the Gâteaux derivative or commutators. This yields a unified formulation of quantum analysis, namely the invariance of quantum derivatives, which are expressed by multiple integrals of ordinary higher derivatives with hyperoperator variables. Multivariate quantum analysis is also formulated in the present unified scheme by introducing a partial inner derivation and a rearrangement formula. Operator Taylo

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22

Bharathi, M. V. L., та K. Jayalakshmi. "Multiplicative δ-derivation in alternative algebras". Asian-European Journal of Mathematics 11, № 04 (2018): 1850051. http://dx.doi.org/10.1142/s1793557118500511.

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Every multiplicative [Formula: see text]-derivation of an alternative algebra [Formula: see text] is additive if there exists an idempotent [Formula: see text] in [Formula: see text] satisfying the following conditions: (i) [Formula: see text] implies [Formula: see text]; (ii) [Formula: see text] implies [Formula: see text]; (iii) [Formula: see text] implies [Formula: see text] for [Formula: see text]. In particular, every [Formula: see text]-derivation of a prime alternative algebra with a nontrivial idempotent is additive. This generalizes the known result obtained by Rodrigues, Guzzo and Fe

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23

BASS, R. W., and A. DEL POPOLO. "DYNAMICAL DERIVATION OF BODE'S LAW." International Journal of Modern Physics D 14, no. 01 (2005): 153–69. http://dx.doi.org/10.1142/s0218271805006195.

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In a planetary or satellite system, idealized as n small bodies in an initially coplanar with concentric orbits around a large central body obeying the Newtonian point-particle mechanics, resonant perturbations will cause a dynamical evolution of the orbital radii except for cases with highly specific mutual relationships. In particular, the most stable situation can be achieved only when each planetary orbit is roughly twice as far from the Sun as the preceding one. This has been empirically observed by Titius (1766) and Bode (1778). By reformulating the problem as a hierarchical sequence of

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24

Amiri, Azita, and Farshid Saeedi. "On pointwise inner derivations of Lie algebras." Asian-European Journal of Mathematics 11, no. 05 (2018): 1850070. http://dx.doi.org/10.1142/s1793557118500705.

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Let [Formula: see text] be a Lie algebra and [Formula: see text] and [Formula: see text] be the set of all derivations and inner derivations of [Formula: see text], respectively. A derivation [Formula: see text] of a Lie algebra [Formula: see text] is pointwise inner if [Formula: see text] for all [Formula: see text]. The set of all pointwise inner derivations of Lie algebra [Formula: see text] denoted by [Formula: see text] form a subalgebra of [Formula: see text] containing [Formula: see text]. In this paper, we prove that, if [Formula: see text] is nilpotent of class [Formula: see text] (so

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25

ALBEVERIO, S., SH A. AYUPOV, K. K. KUDAYBERGENOV, and B. O. NURJANOV. "LOCAL DERIVATIONS ON ALGEBRAS OF MEASURABLE OPERATORS." Communications in Contemporary Mathematics 13, no. 04 (2011): 643–57. http://dx.doi.org/10.1142/s0219199711004270.

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The paper is devoted to local derivations on the algebra [Formula: see text] of τ-measurable operators affiliated with a von Neumann algebra [Formula: see text] and a faithful normal semi-finite trace τ. We prove that every local derivation on [Formula: see text] which is continuous in the measure topology, is in fact a derivation. In the particular case of type I von Neumann algebras, they all are inner derivations. It is proved that for type I finite von Neumann algebras without an abelian direct summand, and also for von Neumann algebras with the atomic lattice of projections, the continuit

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26

Herstein, I. N. "A condition that a derivation be inner." Rendiconti del Circolo Matematico di Palermo 37, no. 1 (1988): 5–7. http://dx.doi.org/10.1007/bf02844264.

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27

Li, Yizheng. "n-derivations of lie color algebras." Filomat 35, no. 9 (2021): 3063–70. http://dx.doi.org/10.2298/fil2109063l.

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The aim of this article is to discuss the n-derivation algebras of Lie color algebras. It is proved that, if the base ring contains 1/n-1, L is a perfect Lie color algebra with zero center, then every triple derivation of L is a derivation, and every n-derivation of the derivation algebra nDer(L)) is an inner derivation.

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BERGEN, JEFFREY. "DERIVATION ALGEBRAS OF RINGS RELATED TO HEISENBERG ALGEBRAS." Journal of Algebra and Its Applications 03, no. 02 (2004): 181–91. http://dx.doi.org/10.1142/s0219498804000794.

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In this paper, we will determine the Lie algebra of derivations of rings which are generalizations of the enveloping algebras of Heisenberg Lie algebras. First, we will determine which derivations are X-inner and also determine which elements in the Martindale quotient ring induce X-inner derivations. Then, we will show that the Lie algebra of derivations is the direct sum of the ideal of X-inner derivations and a subalgebra which is isomorphic to a subalgebra of finite codimension in a Cartan type Lie algebra.

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29

Ferrero, Miguel, Antonio Giambruno, and César Polcino Milies. "A Note on Derivations of Group Rings." Canadian Mathematical Bulletin 38, no. 4 (1995): 434–37. http://dx.doi.org/10.4153/cmb-1995-063-8.

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AbstractLetRGdenote the group ring of a groupGover a semiprime ringR. We prove that, if the center ofGis of finite index and some natural restrictions hold, then everyR-derivation ofRGis inner. We also give an example of a groupGwhich is both locally finite and nilpotent and such that, for every fieldF, there exists anF-derivation ofFGwhich is not inner.

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30

Kadison, Richard V., and Zhe Liu. "Derivations of Murray-von Neumann Algebras." MATHEMATICA SCANDINAVICA 115, no. 2 (2014): 206. http://dx.doi.org/10.7146/math.scand.a-19223.

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A Murray-von Neumann algebra is the algebra of operators affiliated with a finite von Neumann algebra. In this article, we study derivations of Murray-von Neumann algebras and their properties. We show that the "extended derivations" of a Murray-von Neumann algebra, those that map the associated finite von Neumann algebra into itself, are inner. In particular, we prove that the only derivation that maps a Murray-von Neumann algebra associated with a von Neumann algebra of type ${\rm II}_1$ into that von Neumann algebra is 0. This result is an extension, in two ways, of Singer's seminal result

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31

Bergen, Jeffrey, and L. Carini. "Derivations with Invertible Values on a Lie Ideal." Canadian Mathematical Bulletin 31, no. 1 (1988): 103–10. http://dx.doi.org/10.4153/cmb-1988-016-x.

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AbstractLet R be a ring which possesses a unit element, a Lie ideal U ⊄ Z, and a derivation d such that d(U) ≠ 0 and d(u) is 0 or invertible, for all u ∈ U. We prove that R must be either a division ring D or D2, the 2 X 2 matrices over a division ring unless d is not inner, R is not semiprime, and either 2R or 3R is 0. We also examine for which division rings D, D2 can possess such a derivation and study when this derivation must be inner.

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Ber, A., J. Huang, G. Levitina, and F. Sukochev. "Derivations with Values in the Ideal of $$\tau $$-Compact Operators Affiliated with a Semifinite von Neumann Algebra." Communications in Mathematical Physics 390, no. 2 (2022): 577–616. http://dx.doi.org/10.1007/s00220-022-04313-0.

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AbstractLet $${{\mathcal {M}}}$$ M be a semifinite von Neumann algebra with a faithful normal semifinite trace $$\tau $$ τ and let $${{\mathcal {A}}}$$ A be an arbitrary von Neumann subalgebra of $${{\mathcal {M}}}$$ M . We characterize the class of symmetric ideals $${{\mathcal {E}}}$$ E in $${{\mathcal {M}}}$$ M such that derivations $$\delta :{{\mathcal {A}}}\rightarrow {{\mathcal {E}}}$$ δ : A → E are necessarily inner, which is a unification and far-reaching extension of the results due to Johnson and Parrott (J Funct Anal 11:39–61, 1972), due to Kaftal and Weiss (J Funct Anal 62:202–220,

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33

Chirvasitu, Alexandru. "Naturality and innerness for morphisms of compact groups and (restricted) Lie algebras." Proceedings of the American Mathematical Society, Series B 11, no. 25 (2024): 265–76. http://dx.doi.org/10.1090/bproc/164.

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An extended derivation (endomorphism) of a (restricted) Lie algebra L L is an assignment of a derivation (respectively) of L ′ L’ for any (restricted) Lie morphism f : L → L ′ f:L\to L’ , functorial in f f in the obvious sense. We show that (a) the only extended endomorphisms of a restricted Lie algebra are the two obvious ones, assigning either the identity or the zero map of L ′ L’ to every f f ; and (b) if L L is a Lie algebra in characteristic zero or a restricted Lie algebra in positive characteristic, then L L is in canonical bijection with its space of extended derivations (so the latte

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34

LEE, TSIU-KWEN, and YIQIANG ZHOU. "JORDAN *-DERIVATIONS OF PRIME RINGS." Journal of Algebra and Its Applications 13, no. 04 (2014): 1350126. http://dx.doi.org/10.1142/s0219498813501260.

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Let R be a prime ring, which is not commutative, with involution * and with Qms(R) the maximal symmetric ring of quotients of R. An additive map δ : R → R is called a Jordan *-derivation if δ(x2) = δ(x)x* + xδ(x) for all x ∈ R. A Jordan *-derivation of R is called X-inner if it is of the form x ↦ xa - ax* for x ∈ R, where a ∈ Qms(R). We prove that any Jordan *-derivation of R is X-inner if char R ≠ 2 or deg (S(R)) > 4, where S(R) := {x ∈ R|x* = x}.

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35

Ashraf, Mohammad, Shakir Ali, and Bilal Ahmad Wani. "Nonlinear *-Lie Higher Derivations of Standard Operator Algebras." Communications in Mathematics 26, no. 1 (2018): 15–29. http://dx.doi.org/10.2478/cm-2018-0003.

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Abstract Let ℌ be an in finite-dimensional complex Hilbert space and A be a standard operator algebra on ℌ which is closed under the adjoint operation. It is shown that every nonlinear *-Lie higher derivation D = {δn}gn∈N of A is automatically an additive higher derivation on A. Moreover, D = {δn}gn∈N is an inner *-higher derivation.

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36

Kurniadi, Edi. "SIFAT TURUNAN PADA ALJABAR LIE AFFINE BERDIMENSI 6." JURNAL MATEMATIKA MURNI DAN TERAPAN EPSILON 14, no. 1 (2020): 1. http://dx.doi.org/10.20527/epsilon.v14i1.2198.

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In this paper we study that any derivation of affine Lie algebra of dimension 6, denoted by , is inner. We give another approach to prove it by direct computations of transformation matrix of derivation of . We show that transformation matrix for the derivation of any element in equals to transformation matrix of adjoint representation of its element. Furthermore, we give an alternative to prove that is Frobenius Lie algebra. Keywords :Affine Lie algebra, Derivation of a Lie algebra, Frobenius Lie algebra

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37

BAVULA, V. V. "DERIVATIONS AND SKEW DERIVATIONS OF THE GRASSMANN ALGEBRAS." Journal of Algebra and Its Applications 08, no. 06 (2009): 805–27. http://dx.doi.org/10.1142/s0219498809003655.

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Surprisingly, skew derivations rather than ordinary derivations are more basic (important) object in study of the Grassmann algebras. Let Λn = K ⌊x1, …, xn⌋ be the Grassmann algebra over a commutative ring K with ½ ∈ K, and δ be a skew K-derivation of Λn. It is proved that δ is a unique sum δ = δ ev + δ od of an even and odd skew derivation. Explicit formulae are given for δev and δod via the elements δ (x1), …, δ (xn). It is proved that the set of all even skew derivations of Λn coincides with the set of all the inner skew derivations. Similar results are proved for derivations of Λn. In part

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38

Hovatta, Outi. "Derivation of human embryonic stem cell lines, towards clinical quality." Reproduction, Fertility and Development 18, no. 8 (2006): 823. http://dx.doi.org/10.1071/rd06075.

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Human embryonic stem (hES) cells offer an excellent source of cells for transplantation in the treatment of severe diseases. To be clinically safe, the lines have to be derived using strict quality criteria and good manufacturing practice. Animal proteins are immunogenic and may contain microbes, and they should not be used in establishing or propagating hES cells. Derivation systems have been improved towards clinical quality by establishing all 25 hES cell lines using human skin fibroblasts as feeder cells instead of mouse fibroblasts. A further 21 cell lines have been established using synt

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Liang, Xinfeng, and Lingling Zhao. "Bi-Lie n-derivations on triangular rings." AIMS Mathematics 8, no. 7 (2023): 15411–26. http://dx.doi.org/10.3934/math.2023787.

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<abstract><p>The purpose of this article is to prove that every bi-Lie n-derivation of certain triangular rings is the sum of an inner biderivation, an extremal biderivation and an additive central mapping vanishing at $ (n-1)^{th} $-commutators for both components, using the notion of maximal left ring of quotients. As a consequence, we characterize the decomposition structure of bi-Lie n-derivations on upper triangular matrix rings.</p></abstract>

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BAVULA, V. V. "On the eigenvector algebra of the product of elements with commutator one in the first Weyl algebra." Mathematical Proceedings of the Cambridge Philosophical Society 151, no. 2 (2011): 245–62. http://dx.doi.org/10.1017/s0305004111000491.

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Let A1 = K〈X, Y|[Y, X]=1〉 be the (first) Weyl algebra over a field K of characteristic zero. It is known that the set of eigenvalues of the inner derivation ad(YX) of A1 is ℤ. Let A1 → A1, X ↦ x, Y ↦ y, be a K-algebra homomorphism, i.e. [y, x] = 1. It is proved that the set of eigenvalues of the inner derivation ad(yx) of the Weyl algebra A1 is ℤ and the eigenvector algebra of ad(yx) is K〈x, y〉 (this would be an easy corollary of the Problem/Conjecture of Dixmier of 1968 [still open]: is an algebra endomorphism of A1 an automorphism?).

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Rosen, Mary P., and Jerry D. Rosen. "Automorphisms and Derivations of Skew Polynomial Rings." Canadian Mathematical Bulletin 35, no. 1 (1992): 126–32. http://dx.doi.org/10.4153/cmb-1992-018-6.

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AbstractFor a prime ring R and σ ∊ Aut(R), we determine the group of Rstabilizing automorphisms of the skew polynomial ring R[x; σ]. In the case where R is simple, we characterize the X-inner automorphisms of R[x; σ]. We also provide necessary and sufficient conditions for a σ -commuting derivation of a prime ring R to extend to a derivation of R[x; σ].

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NISHIHARA, Takahiro, Masahiro KIYOSUMI, and Hisao SHIIZUKA. "Derivation of Evaluation Items of Inner Branding for Quantitative Method." International Symposium on Affective Science and Engineering ISASE2019 (2019): 1–5. http://dx.doi.org/10.5057/isase.2019-c000050.

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Ebadian, Ali, and Ali Jabbari. "Ultrapowers of Banach algebras." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 9, no. 3 (2022): 527–41. http://dx.doi.org/10.21638/spbu01.2022.313.

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In this paper, we consider ultrapowers of Banach algebras as Banach algebras and the product (J,U) on the second dual of Banach algebras. For a Banach algebra A, we show that if there is a continuous derivation from A into itself, then there is a continuous derivation from (A**,(J,U)) into it. Moreover, we show that if there is a continuous derivation from A into X**, where X is a Banach A-bimodule, then there is a continuous derivation from A into ultrapower of X i. e., (X)U . Ultra (character) amenability of Banach algebras is investigated and it will be shown that if every continuous deriva

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Ren, Li, and Qiang Mu. "A Note on the Cartan Type Lie Superalgebra $\widetilde{S}(n)$ over a Field of Positive Characteristic." Algebra Colloquium 21, no. 03 (2014): 521–26. http://dx.doi.org/10.1142/s1005386714000467.

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The main result of this paper is that every derivation of the finite-dimensional simple modular Lie superalgebra [Formula: see text] is inner, and [Formula: see text] has no nonsingular associative form.

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Rafizadeh, H. A. "Complex force-constant dependence of elastic constants." Canadian Journal of Physics 68, no. 1 (1990): 14–22. http://dx.doi.org/10.1139/p90-003.

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Expressions for the inner and bare components of the elastic constants of crystalline solids are derived. The inner elastic constants are complex functions of the force constants and vanish only for centrosymmetric solids. Using a linear-chain model, the force-constant dependence of inner, bare, and total elastic constants is studied. The linear-chain model is also utilized in derivation of composition-dependent elastic constant equations. Single-parameter and two-parameter theoretical calculations are compared with the experimental composition-dependent Young's moduli of a number of metal–met

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TAMER KOŞAN, M., and TSIU-KWEN LEE. "b-GENERALIZED DERIVATIONS OF SEMIPRIME RINGS HAVING NILPOTENT VALUES." Journal of the Australian Mathematical Society 96, no. 3 (2014): 326–37. http://dx.doi.org/10.1017/s1446788713000670.

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AbstractLet $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}R$ be a semiprime ring with extended centroid $C$ and with maximal right ring of quotients $Q_{mr}(R)$. Let $d{:}\ R\to Q_{mr}(R)$ be an additive map and $b\in Q_{mr}(R)$. An additive map $\delta {:}\ R\to Q_{mr}(R)$ is called a (left) $b$-generalized derivation with associated map $d$ if $\delta (xy)=\delta (x)y+bxd(y)$ for all $x, y\in R$. This gives a unified viewpoint

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Xia, Chunguang, and Wei Wang. "Derivations and Automorphisms of a Lie Algebra of Block Type." Algebra Colloquium 20, no. 01 (2013): 173–80. http://dx.doi.org/10.1142/s1005386713000163.

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Let [Formula: see text] be a Lie algebra of Block type with basis {Lα,i| α ∈ ℤ, i ∈ ℤ+} and relations [Lα,i,Lβ,j]= ((α-1)(j+1)-(β-1)(i+1))Lα+β, i+j. In the present paper, the derivation algebra and automorphism group of [Formula: see text] are explicitly described. In particular, it is shown that the outer derivation space is 1-dimensional and the inner automorphism group of [Formula: see text] is trivial.

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MIRZAVAZIRI, MADJID, and MOHAMMAD SAL MOSLEHIAN. "A KADISON–SAKAI-TYPE THEOREM." Bulletin of the Australian Mathematical Society 79, no. 2 (2009): 249–57. http://dx.doi.org/10.1017/s0004972708001160.

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AbstractSuppose thatσ:𝔐→𝔐 is an ultraweakly continuous surjective *-linear mapping andd:𝔐→𝔐 is an ultraweakly continuous *-σ-derivation such thatd(I) is a central element of 𝔐. We provide a Kadison–Sakai-type theorem by proving that ℌ can be decomposed into${\mathfrak K}\oplus {\mathfrak L}$anddcan be factored as the form$\delta \oplus 2Z\tau $, whereδ:𝔐→𝔐 is an inner *-σ𝔎-derivation,Zis a central element, 2τ=2σ𝔏is a *-homomorphism, andσ𝔎andσ𝔏stand for compressions ofσto 𝔎 and 𝔏 , respectively.

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Ruipu, Bai, Zhang Zhixue, Li Huajun, and Shi Huifen. "The inner derivation algebras of (n+1) dimensional n Lie algebras+." Communications in Algebra 28, no. 6 (2000): 2927–34. http://dx.doi.org/10.1080/00927870008827001.

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Alekseeva, Larisa M., and Svetlana L. Mishlanova. "Metaphor from the Derivational Perspective." Fachsprache 41, S1 (2019): 4–22. http://dx.doi.org/10.24989/fs.v41is1.1780.

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Abstract The article focuses on the derivational perspective of metaphor studies. Derivation is regarded as a complex cognitive process, represented within speech activities. In this sense, derivation is viewed as a universal process of language units’ production according to the rules of text-formation. The basic feature of the derivational approach to the mechanism of metaphor is determined by the inner syntax, especially by the principle of contamination of two sentences – introductive and basic, which fulfill different functions. In this paper we shall present a theoretical account of meta

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