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Independence algebras, basis algebras and semigroups of quotients
Proceedings of the Edinburgh Mathematical Society, 2010AbstractWe show that ifAis a stable basis algebra satisfying thedistributivity condition, thenBis a reduct of an independence algebraAhaving the same rank. If this rank is finite, then the endomorphism monoid ofBis a left order in the endomorphism monoid ofA.
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Leibniz Algebras Admitting a Multiplicative Basis
Bulletin of the Malaysian Mathematical Sciences Society, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Unique Decomposition for Algebras with Multiplicative Basis
Results in MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
S. Bouarroudj +2 more
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The basis of a computer system for modern algebra
Proceedings of the fourth ACM symposium on Symbolic and algebraic computation - SYMSAC '81, 1981So-called general purpose systems for algebraic computation such as ALTRAN, MACSYMA, SAC, SCRATCHPAD and REDUCE are almost exclusively concerned with what is usually known as “classical algebra”, that is, rings of real or complex polynomials and rings of real or complex functions.
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(ANTI)COMMUTATIVE ALGEBRAS WITH A MULTIPLICATIVE BASIS
Bulletin of the Australian Mathematical Society, 2014AbstractA 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, 2019Akivis 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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A basis theorem for matrix algebras
Linear and Multilinear Algebra, 1980Let 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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Basis Theory and Operator Algebras
1997The 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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The Lethal Phenotype of Cancer: The Molecular Basis of Death Due to Malignancy
Ca-A Cancer Journal for Clinicians, 2007Scott A Tomlins +2 more
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