RELATIVE INJECTIVITY OF MODULES AND EXCELLENT EXTENSIONS

Abstract

Let S be an excellent extension of a ring R ₁, M an S-module and N an R-module. It is proved that M _s is an SI-module iff M _R is an SI-module and that N_R is an SI-module iff (N ⊗_R S) is an SI-module. The notions of GV-modules (V-modules, or S ₃ I-modules), hereditary modules and cohereditary modules are also discussed.