Classification of weakly Noetherian monomial algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1085-1089
Voir la notice de l'article provenant de la source Math-Net.Ru
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).
@article{FPM_1995_1_4_a16,
author = {A. Ya. Belov},
title = {Classification of weakly {Noetherian} monomial algebras},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {1085--1089},
publisher = {mathdoc},
volume = {1},
number = {4},
year = {1995},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a16/}
}
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/