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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 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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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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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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One-Sided Ideal Growth of Free Associative Algebras
Monatshefte für Mathematik, 2006For a finitely generated associative algebra over a finite field \(\mathbb{F}_q\), the author defines the left ideal growth as the number \(a_n(R)\) of left ideals \(J\) of codimension \(n\) in \(R\). Similarly, \(m_n(R)\) is the number of maximal left ideals of codimension \(n\).
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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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Fuzzy Translations of Fuzzy Associative Ideals in BCI-algebras
British Journal of Mathematics & Computer Science, 2016The aim of this paper is to introduce the concepts of fuzzy translation to fuzzy associative ideals in BCK/BCI-algebras. Also, the notion of fuzzy extensions and fuzzy multiplications of fuzzy associative ideals with several related properties are investigated.
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Ideals in von Neumann algebras and in associated operator algebras
2015Bibliography: pages 127-130.
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Nonstandard Ideals, Unicellularity, and Algebras Associated with a Shift Operator
1972The shift operator in sequence spaces, its invariant subspaces, and applications of the latter have formed the topic of a host of papers, beginning with the earliest studies of Shilov [1], Beurling [2], and Donoghue [3] and extending up to the fundamental monographs [4, 5] and other recently published works [6–17], which we shall presently discuss in ...
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