Algebras of Finite Self-Injective Dimension

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 1991Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 112, page 619 (issn: 0002-9939,

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Authors: Hoshino, Mitsuo;

doi: 10.2307/2048680 , 10.1090/s0002-9939-1991-1047011-8

Algebras of Finite Self-Injective Dimension

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Abstract

Let A A be an artin algebra. Then A A has finite self-injective dimensions on both sides if and only if every finitely generated left A A -module has finite Gorenstein dimension.

Keywords

Artinian rings and modules (associative rings and algebras), injective dimension, Homological dimension in associative algebras, Artin algebra, Finite rings and finite-dimensional associative algebras, finite Gorenstein dimension, finitely generated left \(A\)-module

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