Publisher Summary This chapter describes the quasi-simple modules and weak transitivity.
If RVD be an R, D-bimodule, where D is a division ring R is a ring and RV is a uniform …

Let R be a commutative ring with identity. For an R-module M, the notion of strongly prime
submodule of M is defined. It is shown that this notion of prime submodule inherits most of …

We study the structure of rings which satisfy the von Neumann regularity of commutators,
and call a ring R C-regular if ab− ba∈(ab− ba) R (ab− ba) for all a, b in R. For a C-regular …

Under study are some conditions for the weakly regular modules to be closed under direct
sums and the rings over which all modules are weakly regular. For an arbitrary right R …

On Secondary Modules Page 1 International Journal of Algebra, Vol. 6, 2012, no. 16, 769 -
774 On Secondary Modules H. Ansari-Toroghy, F. Farshadifar, SS Pourmortazavi and F …

Throughout this paper, $ R $ is an associative ring (not necessarily commutative) with
identity and $ M $ is a right $ R $-module with unitary. In this paper, we introduce a new …

We investigate von Neumann regularity of rings whose simple singular right R-modules are
GP-injective. It is proved that a ring; R is strongly regular iff R is a weakly right duo ring …

arXiv:1609.08054v1 [math.AC] 26 Sep 2016 Page 1 arXiv:1609.08054v1 [math.AC] 26 Sep
2016 1 SOME GENERALIZATIONS OF SECOND SUBMODULES H. ANSARI-TOROGHY AND …

A famous result due to IM Isaacs states that if a commutative ring $ R $ has the property that
every prime ideal is principal, then every ideal of $ R $ is principal. This motivates ring …

ABSTRACT A new notion which is called weakly stable module is introduced in this article. It
is a nontrivial generalization of the modules with endomorphism rings having stable range …