Algebra / Topology Seminar

Speaker: Lars Christensen

TITLE: Injective modules and flat ring extensions

ABSTRACT: Let R --> S be a ring homomorphism. It is an elementary
and well-known fact that given an injective R-module E, the
S-module obtained by co-base change, Hom_R(S,E), is
injective. The converse is not true, not even if $R$ is a commutative
noetherian local domain and S is its completion. In this
setting, it follows from the results I will discuss that an R-module
E with Ext^{>0}_R(S,E) =0 has Hom_R(S,E)<> 0,
and if the S-module Hom_R(S,E) is injective, then E is
injective over R.