TY - JOUR
T1 - Projectively coresolved Gorenstein flat and ding projective modules
AU - Iacob, Alina
N1 - Publisher Copyright:
© 2020, © 2020 Taylor & Francis Group, LLC.
PY - 2020/7/2
Y1 - 2020/7/2
N2 - We give necessary and sufficient conditions in order for the class of projectively coresolved Gorenstein flat modules, (Formula presented.) (respectively that of projectively coresolved Gorenstein (Formula presented.) flat modules, (Formula presented.)), to coincide with the class of Ding projective modules ((Formula presented.) We show that (Formula presented.) if and only if every Ding projective module is Gorenstein flat. This is the case if the ring R is coherent for example. We include an example to show that the coherence is a sufficient, but not a necessary condition in order to have (Formula presented.) We also show that (Formula presented.) over any ring R of finite weak Gorenstein global dimension (this condition is also sufficient, but not necessary). We prove that if the class of Ding projective modules, (Formula presented.) is covering then the ring R is perfect. And we show that, over a coherent ring R, the converse also holds. We also give necessary and sufficient conditions in order to have (Formula presented.) where (Formula presented.) is the class of Gorenstein projective modules.
AB - We give necessary and sufficient conditions in order for the class of projectively coresolved Gorenstein flat modules, (Formula presented.) (respectively that of projectively coresolved Gorenstein (Formula presented.) flat modules, (Formula presented.)), to coincide with the class of Ding projective modules ((Formula presented.) We show that (Formula presented.) if and only if every Ding projective module is Gorenstein flat. This is the case if the ring R is coherent for example. We include an example to show that the coherence is a sufficient, but not a necessary condition in order to have (Formula presented.) We also show that (Formula presented.) over any ring R of finite weak Gorenstein global dimension (this condition is also sufficient, but not necessary). We prove that if the class of Ding projective modules, (Formula presented.) is covering then the ring R is perfect. And we show that, over a coherent ring R, the converse also holds. We also give necessary and sufficient conditions in order to have (Formula presented.) where (Formula presented.) is the class of Gorenstein projective modules.
KW - Ding projective modules
KW - Gorenstein -flat modules
KW - Gorenstein projective modules
KW - projectively coresolved Gorenstein -flat modules
UR - http://www.scopus.com/inward/record.url?scp=85079393894&partnerID=8YFLogxK
U2 - 10.1080/00927872.2020.1723612
DO - 10.1080/00927872.2020.1723612
M3 - Article
AN - SCOPUS:85079393894
SN - 0092-7872
VL - 48
SP - 2883
EP - 2893
JO - Communications in Algebra
JF - Communications in Algebra
IS - 7
ER -