Results 201 to 210 of about 114,095,801 (232)
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Modules and ideals of algebras of associative type
Russian Mathematics, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
N A Koreshkov
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Associated Prime Ideals of the Amalgamated Algebra
Bulletin of the Iranian Mathematical Society, 2022Let \(R\) and \(S\) be commutative rings with unity, \(J\) an ideal of \(S\), and \(f:R\longrightarrow S\) a ring homomorphism. In this paper, the author determines the set of associated prime ideals of amalgamated algebra \(R\bowtie^{f} J\), when \(f\) is surjective. Let \(\mathcal{A}_{1}:= \{p\bowtie^{f}J \mid p\in \mathrm{Ass}(R)\}\); \(\mathcal{A}_{
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On Associator Ideals in Jordan Algebras
Southeast Asian Bulletin of Mathematics, 2000In this paper the authors introduce in a Jordan context the concept of associator semisimple. Let \(J\) be a Jordan algebra over a field of characteristic \(0.\) A subspace \(U\) of \(J\) is said to be an associator ideal of \(J\) if \((U,J,J)\subset U,\) for \((\;, \;, \;)\) the associator of \(J.\) If \(U\) is an associator ideal in \(J\) we can ...
Rema, P. S. +2 more
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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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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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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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