Abstract
An Artin algebra Λ is said to be of finite Cohen–Macaulay type if, up to isomorphism, there are only finitely many indecomposable modules in , the full subcategory of consisting of all Gorenstein projective (right) Λ-modules. In this paper, we study 1-Gorenstein algebras of finite Cohen–Macaulay type through , the category of finitely presented -modules. Some applications will be provided. In particular, a necessary and sufficient condition is given for , the 3 by 3 lower triangular matrices over Λ, to be of finite Cohen–Macaulay type. Finally, the structure of almost split sequences will be described explicitly in a special subcategory of , denoted by . If Λ is self-injective, .
Citation
Rasool Hafezi. Javad Asadollahi. Zohreh Karimi. "On 1-Gorenstein Algebras of Finite Cohen–Macaulay Type." Michigan Math. J. 73 (4) 853 - 873, August 2023. https://doi.org/10.1307/mmj/20216023
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