A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian (all
four combinations are equivalent). The study of these rings grew out of the theory of …

Theorems of Osofsky and Kato imply that a right and left self-injective one-sided perfect ring
is quasi-Frobenius (= QF). The corresponding question for one-sided self-injective one or …

We prove that for a ring $ R $, the following are equivalent:(i) Every right $ R $-module is a
direct sum of extending modules, and (ii) $ R $ has finite type and right colocal type (ie …

Abstract A module M is CS if every submodule of M is essential in a direct summand of M. In
this note we use the CS condition to provide conditions for semiperfect rings to be self …

Structure of some noetherian SI rings Page 1 Journal of Algebra 254 (2002) 362–374 www.academicpress.com
Structure of some noetherian SI rings Dinh Van Huynh Department of Mathematics, Ohio …

A module M is called extending if, for any submodule X of M, there exists a direct summand
of M which contains X as an essential submodule, that is, for any submodule X of M, there …

In 2004, SH Mohamed and BJ Müller defined generalized projectivity (dual ojectivity) as
follows: given modules A and B, A is generalized B-projective (B-dual ojective) if, for any …

A description is given of serial rings whose maximal quotient rings are quasi-Frobenius (QF).
Every serial ring is a factor of a serial ring whose maximal quotient ring is a QF-ring. This …

We discuss some results on CS modules, SI rings, and SC rings. Then we consider the
question of when, over a right SC ring R, every right R-module is CS. In Theorem 3.1 we …

لمصفوفات العكسية كاما ل اشتقاق جوردان اليساري والمركزي على حلقة Jordan Lef Page 1
Shaheeen Iraqi Journal of Science, 2021, Vol. 62, No. 5, pp: 1635-1641 DOI: 10.24996/ijs.2021.62.5.26 …‎