Results 1 to 10 of about 18,642 (313)
Қарағанды университетінің хабаршысы. Математика сериясы, 2023 In recent years there has been a great interest in the study of Zinbiel (dual Leibniz) algebras. Let A be Zinbiel algebra over an arbitrary field K and let e1,e2,...,em,... be a linear basis of A. In 2010 A.
D.M. Zhangazinova, A.S. Naurazbekova
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On the derivations of Leibniz algebras of low dimension
Доповiдi Нацiональної академiї наук України, 2023 Let L be an algebra over a field F. Then L is called a left Leibniz algebra if its multiplication operations [×, ×] addition- ally satisfy the so-called left Leibniz identity: [[a,b],c] = [a,[b,c]] – [b,[a,c]] for all elements a, b, c Î L. In this paper,
L.A. Kurdachenko +2 more
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SYMMETRIC ALGEBRAS OVER RINGS AND FIELDS [PDF]
Bulletin of the Australian Mathematical Society, 2013 AbstractConnections between annihilators and ideals in Frobenius and symmetric algebras are used to provide a new proof of a result of Nakayama on quotient algebras, and an application is given to central symmetric algebras.
Craven, Thomas, Smith, Tara
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On the Lie structure of locally matrix algebras
Karpatsʹkì Matematičnì Publìkacìï, 2020 Let $A$ be a unital locally matrix algebra over a field $\mathbb{F}$ of characteristic different from $2.$ We find a necessary and sufficient condition for the Lie algebra $A\diagup\mathbb{F}\cdot 1$ to be simple and for the Lie algebra of derivations ...
O. Bezushchak
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Deformations of the three-dimensional Lie algebra sl(2)
Қарағанды университетінің хабаршысы. Математика сериясы, 2020 Deformation is one of key questions of the structural theory of algebras over a field. Especially, it plays a important role in the classification of such algebras.
A.A. Ibrayeva +2 more
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Algebraic complexities and algebraic curves over finite fields [PDF]
Journal of Complexity, 1987 We consider the problem of minimal (multiplicative) complexity of polynomial multiplication and multiplication in finite extensions of fields. For infinite fields minimal complexities are known [Winograd, S. (1977) Math. Syst. Theory 10, 169-180].
David V. Chudnovsky +1 more
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M-Hazy Vector Spaces over M-Hazy Field
Mathematics, 2021 The generalization of binary operation in the classical algebra to fuzzy binary operation is an important development in the field of fuzzy algebra. The paper proposes a new generalization of vector spaces over field, which is called M-hazy vector spaces
Faisal Mehmood, Fu-Gui Shi
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ASSOCIATIVE NIL-ALGEBRAS OVER FINITE FIELDS [PDF]
International Journal of Algebra and Computation, 2013 We study the nilpotency degree of a relatively free finitely generated associative algebra with the identity xn = 0 over a finite field 𝔽 with q elements. In the case of q ≥ n the nilpotency degree is proven to be the same as in the case of an infinite field of the same characteristic.
Artem A. Lopatin, Ivan P. Shestakov
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Gröbner bases over algebraic number fields [PDF]
Proceedings of the 2015 International Workshop on Parallel Symbolic Computation, 2015 Although Buchberger's algorithm, in theory, allows us to compute Gröbner bases over any field, in practice, however, the computational efficiency depends on the arithmetic of the ground field. Consider a field $K = \mathbb{Q}(α)$, a simple extension of $\mathbb{Q}$, where $α$ is an algebraic number, and let $f \in \mathbb{Q}[t]$ be the minimal ...
Dereje Kifle Boku +3 more
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On the derivations of cyclic Leibniz algebras
Karpatsʹkì Matematičnì Publìkacìï, 2022 Let $L$ be an algebra over a field $F$. Then $L$ is called a left Leibniz algebra, if its multiplication operation $[-,-]$ additionally satisfies the so-called left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,c\in L$. A linear
M.M. Semko, L.V. Skaskiv, O.A. Yarovaya
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