A module M is called dual-square-free (DSF) if M has no proper submodules A and B with
M= A+ B and M/A≅ M/B. The class of DSF-modules is closed under direct summands and …

A module M is called dual-square-free (DSF) if M has no proper submodules A and B with
M= A+ B and M/A≅ M/B. The class of DSF-modules is closed under direct summands and …

ABSTRACT A module M is said to be square free if whenever its submodule is isomorphic to
N 2= N⊕ N for some module N, then N= 0. Dually, a module M is said to be d-square free …

A ring R is called a left (right) SF-ring if all simple left (right) R-modules are flat. This concept
was introduced by VS Ramamurthi [a]. It is still an open question whether or not a left (or two …

Let R be a ring with minimum condition on left or right ideals. It is shown that R is a QF⋅ 3
ring if and only if each finitely generated submodule of the injective hull of R, regarded as a …

1.1. We denote by End (M), J (M), max (M), and Lat (M)) the endomorphism ring, the:
lacobson radical, the set of all maximal submodules, and the lattice of all submodules of a …

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 …

A ring R with identity is called left QF-3'if the injective hull E (R) of the left i?-module R is
torsionless. This class of rings and the other related generalizations of quasi-Frobenius rings …

Several papers find conditions on a ring R in order for certain properties of modules to be
preserved under direct sums, and direct products. Thus we know when direct sums of …

In this paper we study when a unital right module M over a ring R with identity has a special
“small image” property we call (S*): namely, M has (S*) if every submodule N of M contains a …