Preface All rings are assumed to be associative and (except for nilrings and some stipulated
cases) to have nonzero identity elements. A ring A is said to be regular if for every element a …

We define and investigate t-semisimple modules as a generalization of semisimple
modules. A module M is called t-semisimple if every submodule N contains a direct …

All rings are assumed to be associative and (except for nil-rings and some stipulated cases)
to have nonzero identity elements. Expressions such as a “Noetherian ring” mean that the …

Publisher Summary This chapter discusses the max rings, V-rings, and rings and modules
related to V-rings. All rings are associative and have nonzero identity elements. A module is …

Let M be a right R-module. Define Z (N)(8 M (N)) to be the set of elements ne N for any R-
module N in a [M] such that nR is an M-small (respectively 8-M-small) modüle. In this note it …

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 MR is an SI-module and that NR is an SI-module iff (N⊗ …

M (N)(δ∗ M (N)) to be the set of elements n∈ N for any R-module N in σ [M] such that nR is
an M-small (respectively δ-M-small) module. In this note it is proved that M is a GCO-module …