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- Title
Pure-injectivity in the category of Gorenstein projective modules.
- Authors
Yu, Peng; Huang, Zhaoyong
- Abstract
In this paper, we introduce and study (weak) pure-injective Gorenstein projective modules. Let be an Artin algebra. We prove that the category of weak pure-injective Gorenstein projective left -modules coincides with the intersection of the category of pure-injective left -modules and that of Gorenstein projective left -modules. Then, we get an equivalent characterization of virtually Gorenstein algebras (being CM-finite). Furthermore, we prove that the category of weak pure-injective Gorenstein projective left -modules is enveloping in the category of left -modules; and if is virtually Gorenstein, then it is precovering in the category of pure-injective left -modules.
- Subjects
MODULES (Algebra); GORENSTEIN rings; ARTIN algebras; REPRESENTATION theory; HOMOLOGICAL algebra
- Publication
Journal of Algebra & Its Applications, 2017, Vol 16, Issue 8, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498817501468