Classification of weakly Noetherian monomial algebras

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We describe weakly Noetherian (i.e. satisfying the ascending chain condition on two-sided ideals) monomial algebras as follows. Let AA be a weakly Noetherian monomial algebra. Then there exists a Noetherian set of (super-)words UU such that every non-zero word in AA is a subword of a word belonging to UU. A finite set of words or superwords UU is said to be Noetherian, if every element of UU 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).
Original languageAmerican English
Pages (from-to)1085-1089
JournalFundamentalnaya i Prikladnaya Matematika (Moscow)
Issue number4
StatePublished - 1995

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