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 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

 Fundam. Prikl. Mat., 1995, Volume 1, Issue 4, Pages 1085–1089 (Mi fpm106)

Short communications

Classification of weakly Noetherian monomial algebras

A. Ya. Belov

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Abstract: We describe weakly Noetherian (i.e. satisfying the ascending chain condition on two-sided ideals) monomial algebras as follows. Let $A$ be a weakly Noetherian monomial algebra. Then there exists a Noetherian set of (super-)words $\mathcal U$ such that every non-zero word in $A$ is a subword of a word belonging to $\mathcal U$. A finite set of words or superwords $\mathcal U$ is said to be Noetherian, if every element of $\mathcal U$ is either a finite word or a product of a finite word and one or two uniformly-recurring superwords (in the last case one of these superwords is infinite to the left and the other one to the right).

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Bibliographic databases:
UDC: 512.552.4+512.554.32+512.664.2

Citation: A. Ya. Belov, “Classification of weakly Noetherian monomial algebras”, Fundam. Prikl. Mat., 1:4 (1995), 1085–1089

Citation in format AMSBIB
\Bibitem{Bel95}
\by A.~Ya.~Belov
\paper Classification of weakly Noetherian monomial algebras
\jour Fundam. Prikl. Mat.
\yr 1995
\vol 1
\issue 4
\pages 1085--1089
\mathnet{http://mi.mathnet.ru/fpm106}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1791631}
\zmath{https://zbmath.org/?q=an:0868.16015}