Introduction: All rings in this paper are associative and have an identity. All modules will be
daitary. Let R be any ring and M a left R-module. A submodule N of M is called essential if …

The submodules with the property of the title (N⊆ M is strongly essential in M if∏ IN is
essential in∏ IM for any index set I) are introduced and fully investigated. It is shown that for …

An extension ring S of a ring T is called a left quotient ring of T if for any two elements ΛH= 0
and y of S there exists an element a of T such that ax^ rO and ay belongs to T. Let R be a …

We study the class of almost uniserial rings as a straightforward common generalization of
left uniserial rings and left principal ideal domains. A ring R is called almost left uniserial if …

By an essential product of two rings is meant a subdirect product which contains an
essential right ideal of the direct product. The aim of this paper is to investigate the utility of …

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 …

All rings are assumed to be associative and to have a nonzero identity element. Let A be a
ring, and let M be a right A-module. A proper ideal P of the ring A is said to be right primitive …

Rings over which every nonzero right module has a maximal submodule are called right
Bass rings. For a ring A module-finite over its center C, the equivalence of the following …

Throughout, we assume all rings are associative with identity and all modules are unitary.
See [7] for undefined terms and [3] for all homological concepts. Let R be a ring, E (R) the …

An element k of a ring R is called left minimal if Rk is a minimal left ideal of R. A ring R is
called a left strongly DS, DS ring and MFS ring, respectively if for every left minimal element …