TY - JOUR
T1 - Injective modules under faithfully flat ring extensions
AU - Winther, Lars
AU - Köksal, Fatih
N1 - Publisher Copyright:
© 2015 American Mathematical Society.
PY - 2016/3
Y1 - 2016/3
N2 - Let R be a commutative ring and let S be an R-algebra. It is wellknown that if N is an injective R-module, then HomR(S,N) is an injective S-module. The converse is not true, not even if R is a commutative noetherian local ring and S is its completion, but it is close: It is a special case of ourmain theorem that, in this setting, an R-module N with Ext>0 R (S,N) = 0 is injective if HomR(S,N) is an injective S-module.
AB - Let R be a commutative ring and let S be an R-algebra. It is wellknown that if N is an injective R-module, then HomR(S,N) is an injective S-module. The converse is not true, not even if R is a commutative noetherian local ring and S is its completion, but it is close: It is a special case of ourmain theorem that, in this setting, an R-module N with Ext>0 R (S,N) = 0 is injective if HomR(S,N) is an injective S-module.
KW - Co-base change
KW - Faithfully flat ring extension
KW - Injective module
UR - http://www.scopus.com/inward/record.url?scp=84954551613&partnerID=8YFLogxK
U2 - 10.1090/proc/12791
DO - 10.1090/proc/12791
M3 - Article
AN - SCOPUS:84954551613
SN - 0002-9939
VL - 144
SP - 1015
EP - 1020
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 3
ER -