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- W4298230023 abstract "An Artin algebra $Lambda$ is said to be of finite Cohen-Macaulay type, $rm{CM}$-finite for short, if the full subcategory $rm{Gprj}mbox{-} Lambda$ of finitely generated Gorenstein projective $Lambda$-modules is of finite representation type. If $Lambda$ is a $rm{CM}$-finite algebra, then we denote by $rm{Aus}(underline{rm{Gprj}}mbox{-} Lambda)$ the stable Cohen-Macaulay Auslander algebra, i.e. $rm{underline{End}}_{Lambda}(G)$, where $G $ is a basic representation generator of $rm{Gprj}mbox{-}Lambda$. In this paper, we will explain how by defining an equivalence relation on the elements of algebra $rm{Aus}(underline{rm{Gprj}}mbox{-} Lambda)$ can be used to give a characterization for $rm{Aus}(underline{rm{Gprj}}mbox{-} Lambda)$ to be of finite representation type, or equivalently, the $rm{CM}$-finiteness of the algebra of $2 times 2$ lower triangular matrices over $Lambda,$ where $Lambda$ is a $rm{CM}$-finite Artin algebra over an algebraic closed filed. Then, by presenting some examples we will show how our results work." @default.
- W4298230023 created "2022-10-01" @default.
- W4298230023 creator A5047826494 @default.
- W4298230023 date "2018-05-23" @default.
- W4298230023 modified "2023-09-26" @default.
- W4298230023 title "A ring theoretic approach to the finite representation type" @default.
- W4298230023 doi "https://doi.org/10.48550/arxiv.1805.09062" @default.
- W4298230023 hasPublicationYear "2018" @default.
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