A module $ M $ is called a CS module if every submodule of $ M $ is essential in a direct
summand of $ M $. A ring $ R $ is said to be right (countably) $\Sigma $-CS if any direct sum …

A module is serial if its submodules are linearly ordered with respect to inclusion. A ring R is
called left serial if RR is a direct sum of serial modules, and R is called serial if it is both left …

In this paper we shall characterize the generators whose endomorphism rings are serial
Noetherian. A module is serial when its submodules are linearly ordered with respect to …

A module is called automorphism-invariant if it is invariant under any automorphism of its
injective hull. In [Algebras for which every indecomposable right module is invariant in its …

We shall call a ring R a left IF ring if every injective left R-module is flat. The purpose of this
paper is to characterize left and two-sided IF rings in several ways and to give some …

Let J? be a ring with unit element. We always consider unitary right R-modules. Let T be an
jR-module and η a cardinal number. If for any module K containing T as a direct summand …

All rings have a unit element and all modules are unitary. If R is a ring and if A is a subring of
R (containing the unit element of/?), then we may consider R äs a left (resp. a right)^ 4 …

A non-singular R-module M is a ray for the class of all non-singular modules if every R-
homogeneous map from M into a non-singular module is additive. Every essential extension …

A submodule N of a module M is called S-closed (in M) if M/N is nonsingular. It is well-known
that the class Closed of short exact sequences determined by closed submodules is a …

Cukerman [2], Shanny [5], and Ware [7] have shown that a ring R is Artin semisimple if and
only if R has a nonfinitely generated free module with regular endomorphism ring. This …