Proposition 1: a) M has SIP if and only if for every pair ofsummands S and T with TT: M+ S
the projection map, the kernel of the restricted map vIT is a summand. b) If M has SIP and S c …

In this note, developing our previous work [8] with S. Takashima, we will characterize rings R
for which every finitely generated submodule of the injective envelope E (RR) is torsionless …

Let M be a left module, over a ring R. M is called a Zelmanowitz-regular module if for each
x∊ M there exists a homomorphism f: M→ R such that f (x) x= x. Let Q be a left R-module and …

A module is defined to be an automorphism-invariant module if it is invariant under
automorphisms of its injective hull. Quasi-injective modules and, more generally, pseudo …

EPIMORPHISMS OF MODULES WHICH MUST BE ISOMORPHISMS Page 1 Canad. Math.
Bull. Vol. 16 (4), 1973 EPIMORPHISMS OF MODULES WHICH MUST BE ISOMORPHISMS BY …

Let cp be a ring homomorphism from a ring R to a ring Q. If Q is flat as a right R-module and
q is a ring epimorphism, we say that QR is a flat epimorphism. If Q is projective with respect …

Automorphism-extendable modules Page 1 Discrete Math. Appl. 2015; 25 (5):305–309 Askar
A. Tuganbaev Automorphism-extendable modules Abstract: We study modules, in which all …

Let A be an integral domain and R its field of fractions. An A-module E is said to be torsion
free if ox= 0 for ctEA, xEE implies a= 0 or x= 0. We will say that a submodule£ i of an A …

This review paper is concerned with modules in which all automorphisms (endomorphisms)
of submodules can be extended to endomorphisms of the entire module. We consider old …

In [2, Ch. VIII,? 5 and? 6] theorems on chains of syzygies were proved for graded rings and
for local rings by a unified method based on the notions of" faithful system"," proper module" …