Two obvious classes of quasi-injective modules are those of semisimples and injectives. In
this paper, we study rings with no quasi-injective modules other than semisimples and …

Let R be a ring. A right R-module C is called a cotorsion module if Ext1R (F, C)= 0 for any flat
right R-module F. In this paper, we first characterize those rings satisfying the condition that …

We introduce and study the notion of wd-Rickart modules (ie modules M such that for every
nonzero endomorphism ϕ of M, the image of ϕ contains a nonzero direct summand of M) …

All rings are assumed to be associative and (except for nil-rings and some stipulated cases)
to have nonzero identity elements. Expressions such as a “Noetherian ring” mean that the …

The notation in this paper will be standard and it may be found in [2] or [8]. Throughout the
paper, the notation A⊂'B will mean that A is an essential submodule of the module B. Given …

We prove that if R is a right semi-Artinian ring, then R is an exchange ring and every
irredundant set Simp R of representatives of simple right R-modules carries a canonical …

The well known Schröder–Bernstein Theorem states that any two sets with one to one maps
into each other are isomorphic. The question of whether any two (subisomorphic or) direct …

Let R be a ring. A right R-module M is called “essentially compressible” if it embeds in each
of its essential submodules. Also a module XR is called “completely essentially …

We introduce and investigate weak relative Rickart objects and dual weak relative Rickart
objects in abelian categories. Several types of abelian categories are characterized in terms …

ON SOME CLASSES OF SEMIARTINIAN RINGS Page 1 Siberian Mathematical Journal, Vol.
53, No. 5, pp. 763–771, 2012 Original Russian Text Copyright c 2012 Abyzov AN ON SOME …