Results 281 to 290 of about 21,477 (310)

(ANTI)COMMUTATIVE ALGEBRAS WITH A MULTIPLICATIVE BASIS

Bulletin of the Australian Mathematical Society, 2014
AbstractA basis ${\mathcal{B}}=\{u_{i}\}_{i\in I}$ of a commutative or anticommutative algebra $\mathfrak{C},$ over an arbitrary base field $\mathbb{F}$, is called multiplicative if for any $i,j\in I$ we have that $u_{i}u_{j}\in \mathbb{F}u_{k}$ for some $k\in I$.
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A Linear Basis of the Free Akivis Algebra

Journal of Mathematical Sciences, 2019
Akivis algebras were introduced in 1976, by \textit{M. A. Akivis} in the paper [Sib. Math. J. 17, 3--8 (1976; Zbl 0337.53018); translation from Sibir. Mat. Zh. 17, 5--11 (1976)]. Let \(F(X)\) be the free nonassociative algebra over a field \(K\) with the set \(X\) of free generators.
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Division algebras with a projective basis

Israel Journal of Mathematics, 2001
The authors study Schur algebras with a projective basis, i.e. central simple \(k\)-algebras which are isomorphic to a twisted group algebra over \(k\). Their main results are as follows: 1. If the twisted group algebra \(k^\alpha G\) is a division algebra with centre \(k\), then the commutator subgroup of \(G\) is cyclic. Moreover 2.
Aljadeff, Eli, Haile, Darrell
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A basis theorem for matrix algebras

Linear and Multilinear Algebra, 1980
Let F be a field and let M n(F) denote the algebra of n×n matrices over F. Let P∈Mn (F) be such that its characteristic polynomial is irreducible in F[x]. We show that if Q∈Mn (F) has rank one, then {Pi Qj |⩽i,j⩽n-1} is a basis for Mn (F). (The fact that P,Q generate Mn (F), while being a consequence of this result, is easily established independently;
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Algebraic Basis of the Algebra of All Symmetric Continuous Polynomials on the Cartesian Product of ℓp-Spaces

Axioms, 2022
Andriy Bandura, Viktoriia Kravtsiv, Taras Vasylyshyn   +2 more
exaly  

An integral basis for algebraic fields

Mathematical Notes of the Academy of Sciences of the USSR, 1973
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Basis Theory and Operator Algebras

1997
The interaction of operator theory and basis theory has provided stimulation to both disciplines. Various types of bases have been used to give interesting examples and counterexamples of non-selfadjoint operator algebras. In the opposite direction, operator theorists have shown that pathologies which were previously known only in specially constructed
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Two kinds of B-basis of the algebraic hyperbolic space

Journal of Zhejiang University: Science A, 2005
Wang Guo-Zhao, Guo-Zhao Wang
exaly  

Algebraic Chase Decoding of Elliptic Codes Through Computing the Gröbner Basis

2022
Fangguo Zhang, Yunqi Wan
exaly  

The Basis for Geometric Algebra

2006
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