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Gorenstein injective envelopes and covers over two sided noetherian rings
- Source :
- Communications in Algebra. 45:2238-2244
- Publication Year :
- 2016
- Publisher :
- Informa UK Limited, 2016.
-
Abstract
- We prove that the class of Gorenstein injective modules is both enveloping and covering over a two sided noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat. In the second part of the paper we consider the connection between the Gorenstein injective modules and the strongly cotorsion modules. We prove that when the ring R is commutative noetherian of finite Krull dimension, the class of Gorenstein injective modules coincides with that of strongly cotorsion modules if and only if the ring R is in fact Gorenstein.
- Subjects :
- Noetherian
Noetherian ring
Pure mathematics
Class (set theory)
Algebra and Number Theory
Mathematics::Commutative Algebra
Mathematics::Rings and Algebras
010102 general mathematics
Mathematics - Rings and Algebras
Mathematics - Commutative Algebra
Commutative Algebra (math.AC)
01 natural sciences
Injective function
Mathematics::Algebraic Geometry
Character (mathematics)
Rings and Algebras (math.RA)
0103 physical sciences
FOS: Mathematics
18G10, 18G25, 18G35
010307 mathematical physics
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 15324125 and 00927872
- Volume :
- 45
- Database :
- OpenAIRE
- Journal :
- Communications in Algebra
- Accession number :
- edsair.doi.dedup.....e5def49002b9453e4b1c6f29c3aa0a57