TY - JOUR
T1 - Gorenstein injective envelopes and covers over two sided noetherian rings
AU - Iacob, Alina
N1 - Publisher Copyright:
© 2017, Copyright © Taylor & Francis.
PY - 2017/5/4
Y1 - 2017/5/4
N2 - 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.
AB - 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.
KW - Gorenstein injective cover
KW - Gorenstein injective envelope
KW - Gorenstein injective module
KW - strongly cotorsion module
UR - http://www.scopus.com/inward/record.url?scp=85006110332&partnerID=8YFLogxK
U2 - 10.1080/00927872.2016.1233193
DO - 10.1080/00927872.2016.1233193
M3 - Article
SN - 0092-7872
VL - 45
SP - 2238
EP - 2244
JO - Communications in Algebra
JF - Communications in Algebra
IS - 5
ER -