We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Pure-semisimplicity of the category of graded modules over graded artin algebras.
- Authors
Mahdavi, Elham; Vahed, Razieh
- Abstract
Let Λ be a ℤ -graded artin algebra. It is proved that the category of graded Λ -modules is pure-semisimple if and only if there are only finitely many nonisomorphic indecomposable finitely generated graded Λ -modules. As a consequence of this result together with a known result of Gordon and Green (which states that Λ is of finite representation type if and only if there are only finitely many non-isomorphic indecomposable finitely generated graded Λ -modules), we see that the category of all Λ -modules is pure-semisimple if and only if the category of all graded Λ -modules is so.
- Subjects
ARTIN algebras; REPRESENTATIONS of algebras
- Publication
Journal of Algebra & Its Applications, 2023, Vol 22, Issue 7, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498823501499