Results 11 to 20 of about 11,402 (264)
Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
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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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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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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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Unimodular rows over affine algebras over algebraic closure of a finite field
Journal of Algebra and Its Applications, 2022 In this paper, we prove that if [Formula: see text] is an affine algebra of dimension [Formula: see text] over [Formula: see text] and [Formula: see text] then any unimodular row over [Formula: see text] of length [Formula: see text] can be mapped to a factorial row by elementary transformations.
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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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Normal Division Algebras Over a Modular Field [PDF]
Transactions of the American Mathematical Society, 1934 and that there exist inseparable extensions F(x) of F if and only if some quantity a of F is not the pth power of any quantity of F. An infinite field F is called perfect if either F is non-modular or every quantity of F has the form fP where p is the characteristic of F and f is in F.
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Existence of Split Property in Quaternion Algebra Over Composite of Quadratic Fields
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Quaternions are extensions of complex numbers that are four-dimensional objects. Quaternion consists of one real number and three complex numbers, commonly denoted by the standard vectors and .
Muhammad Faldiyan +2 more
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