Results 111 to 120 of about 117,907,174 (136)
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On the Action of Derivations on Nilpotent Ideals of Associative Algebras
Ukrainian Mathematical Journal, 2009Summary: Let \(I\) be a nilpotent ideal of an associative algebra \(A\) over a field \(F\) and let \(D\) be a derivation of \(A\). We prove that the ideal \(I+D(I)\) is nilpotent if \(\text{char\,}F=0\) or the nilpotency index \(I\) is less than \(\text{char\,}F=p\) in the case of positive characteristic of the field \(F\). In particular, the sum \(N(A)
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On the Complexity Functions for T-Ideals of Associative Algebras
Mathematical Notes, 2000Let \(c_n({\mathbf V})\), \(n=0,1,2,\dots\), be the codimension sequence of the variety \(\mathbf V\) of associative algebras over an arbitrary field \(K\). The author considers the exponential generating function \({\mathcal C}({\mathbf V},z)=\sum_{n\geq 0}c_n({\mathbf V})z^n/n!\) known also as the complexity function of \(\mathbf V\) [see the book of
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Fuzzifications of Foldness of Quasi-Associative Ideals inBCI-Algebras
Journal of Applied Mathematics and Computing, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Young Bae Jun, Kyung Ho Kim
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Lie ideals of graded associative algebras
Israel Journal of Mathematics, 2011In the paper under review the authors translate some results of quotients of Lie structures to the graded case. Let \(G\) be a group. A (general) algebra \(S\) over a ring of scalars \(\phi\) is \(G\)-graded if \(S=\bigoplus_{\sigma\in G} S_\sigma\), where \(S_\sigma\) is a submodule of \((S, +)\) and \(S_\sigma S_\tau \subset S_{\sigma\tau}\) for ...
Bierwirth, Hannes +1 more
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Ideals in the Multiplication Algebra of a Non-Associative K-Algebra
Communications in Algebra, 1993For a non-associative K-algebraA, and σ ∊ A there are K Vector space morphisms L σ : A → A and R σ : A → A given ...
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Extensions of ideals in associative algebras
Mathematical Proceedings of the Cambridge Philosophical Society, 19591. Let A be an associative algebra over a commutative field K; A is then a vector space over K, and multiplication is defined in A in such a way thatfor x, y, z in A and λ in K. We suppose in addition that A does not contain a unit, and we denote by Ae the algebra obtained by adjoining a unit e to A.
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On Tractability and Ideal Problem in Non-Associative Operator Algebras
Integral Equations and Operator Theory, 2010The paper centers around the following problem by \textit{W.\,Wojtyński} [Bull.\ Acad.\ Polon.\ Sci.\ 24, 797--801 (1976; Zbl 0356.47015)]: Does every closed Lie algebra of compact quasinilpotent operators on a Banach space contain a non-trivial closed Lie ideal?
Brešar, Matej +2 more
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Bases for the Prime Ideals Associated with Certain Classes of Algebraic Varieties
Mathematical Proceedings of the Cambridge Philosophical Society, 1943The fact that the prime ideal associated with a given irreducible algebraic variety has a finite basis is a pure existence theorem. Only in a few isolated particular cases has the base for the ideal been found, and there appears to be no general method for determining the base which can be carried out in practice.
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Power-Associative Algebras in which Every Subalgebra is a Left Ideal
Canadian Mathematical Bulletin, 1970By an L-algebra we mean a power-associative nonassociative algebra (not necessarily finite-dimensional) over a field F in which every subalgebra generated by a single element is a left ideal.
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