A basic tool in the usual presentation of the Morita theorems is the correspondence theorem
for projective modules. Let RM be a left R-module and B= HomR (M, M). When M is a …

Publisher Summary This chapter describes the perfect projectors and perfect injectors. It is
assumed that R and S are rings and R m and S m are the categories of all left R-modules …

Let M be a left module over a ring R. A submodule N of M is called locally split in M if for
each x EN there exists a homomorphism h: Mt N such that h (x)= x. It is shown that if N is …

Let $ R $ and $ S $ be rings with unit. Suppose $ P $ is a free $ R $-module on $\beta $
generators, where $\beta $ is an infinite cardinal number not smaller than the cardinality of …

In this note we shall use the same notations and terminologies as in [2]. In [2] we proved that,
if R is a weakly noetherian ring for which dim (mspec (R)) is finite, any nonfinitely generated …

The primary goal of this paper is to investigate the structure of irreducible monomorphisms to
and irreducible epimorphisms from finitely generated free modules over a noetherian local …

We prove that each almost local-global semihereditary ring R has the stacked bases
property and is almost Bézout. More precisely, if M is a finitely presented module, its torsion …

ABSTRACT A module M Is said to be weakly projective If and only If It has a projective cover
11": P (M)--+ M and every map from P (M) Into a finitely generated (free) module can be …

Projectivity and flatness over the endomorphism ring of a finitely generated module Page 1
IJMMS 2004:30, 1581–1588 PII. S0161171204310082 http://ijmms.hindawi.com © Hindawi …

A module M is called semiprojective if for any epimorphism h: MM and any f~ End~ there
exists f~ EndM such that fh= hr. A rip~ g is called bounded if each essential one-sided ideal …