TY - JOUR

T1 - Injective modules under faithfully flat ring extensions

AU - Winther, Lars

AU - Köksal, Fatih

N1 - Publisher Copyright:
© 2015 American Mathematical Society.
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

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

VL - 144

SP - 1015

EP - 1020

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -