A ring R is a right SI-ring if every singular right R-module is injective, while R is a right S3I-
ring if every singular semisimple right R-module is injective. In this paper, we investigate and …

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 …

A theorem due to Warfield states that “a ring R is left serial if and only if every (finitely
generated) projective left R-module is serial” and a theorem due to Tuganbaev states that “a …

The concepts of Tor-prime and Strongly Tor-prime submodules are introduced and
investigated. A proper submodule N is called Tor-prime submodule (resp. Strongly prime), if …

Let R be an arbitrary ring with identity and M a right R-module. In this paper, we introduce a
class of modules which is an analogous of δ-supplemented modules defined by Kosan. The …

In this thesis, for some classes of rings including, local, semilocal right semihereditary and
right Noetherian right nonsingular, we obtain some conditions that equivalent to being right …

In this paper we continue our study about quasi-primary submodules (probably satisfying the
primeful property), that was defined and studied in Part I (see [8]). We define a quasi-primary …

Primary-like and weakly primary-like submodules are two new generalizations of primary
ideals from rings to modules. In fact, the class of primary-like submodules of a module lie …

It is known that every essential extension of a direct sum of injective hulls of simple R-
modules is a direct sum of injective R-modules if and only if the ring R is right noetherian …

Let $ R $ be a commutative ring with a non-zero identity, $ S $ be a multiplicatively closed
subset of $ R $ and $ M $ be a unital $ R $-module. In this paper, we define a submodule …