Geodesic
Classification of weakly Noetherian monomial algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1085-1089.

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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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A. Ya. Belov. Classification of weakly Noetherian monomial algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1085-1089. http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a16/

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