Consider a l-dim commutative reduced noetherian ring R so that the integral closure of R in
its total quotient ring is a finitely generated R-module, and let A= R [X,,..., X,] be the …

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 …

All rings are assumed to be associative with nonzero unity, all modules are unitary and
unless the side is specified, right. A module with a distributive lattice of submodules is called …

Let RP be a projective R-module which is not finitely generated. Let E= End R (P). This
paper examines the structure of P as an E-module and relations between right ideals of R …

We identify a large class of rings over which locally free modules are determined by their
endomorphism rings. We characterize these endomorphism rings and consider under what …

ABSTRACT A principal right ideal of a ring is called uniquely generated if any two elements
of the ring that generate the same principal right ideal must be right associated (ie, if for all a …

Abstract A right R-module M is said to be finendo provided that as a left module over its
endomorphism ring it is finitely generated. Let B= End MR. Then B n→ M→ 0 is exact for …

The notion of generalized projective covers Is Introduced to give a natural generalization of
a theorem of Bass on perfect rings. Moreover, In terms of this notion, some characterizations …

In this paper, we introduce and study the pure-direct-projective modules, that is the modules
M every pure submodule A of which with M/A isomorphic to a direct summand of M is a direct …

Essential Extensions of a Direct Sum of Simple Modules-II Page 1 Modules and Comodules
Trends in Mathematics, 243–246 c© 2008 Birkhäuser Verlag Basel/Switzerland Essential …