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 …

We study the class of virtually uniserial modules and rings as a nontrivial generalization of
uniserial modules and rings. An R-module M is virtually uniserial if for every finitely …

Let R be a ring. The ring R is called right almost nil-injective, if for any a∈ N (R), there exists
a left ideal Xa of R such that lr (a)= Ra⊕ Xa. In this paper, we give some characterizations …

A unitary left R-module M over a left noetherian ring R with identity is called admissible if
every prime ideal of R, which is the left annihilator of all nonzero submodules of a …

A result of Ginn and Moss asserts that a left and right noetherian ring with essential right
socle is left and right artinian. There are examples of right finitely embedded rings with ACC …

All rings have a unit element and all modules are unitary. If R is a ring and if A is a subring of
R (containing the unit element of/?), then we may consider R äs a left (resp. a right)^ 4 …

Theorem (K6the-Cohen-Kaplansky). A commutative ring R has the property that each of its R-
modules is a direct sum of cyclic modules if and only if R is an artinian principal ideal ring …

All rings R considered in this note are associative and have an identity. A module M is a
unitary left R-module, E (M)=-E,(M) denotes its injective hull, and Ass (M) is the set of its …

A ring R is called left IP-injective if every homomorphism from a left ideal of R into R with
principal image is given by right multiplication by an element of R. It is shown that R is left IP …

In this article, we call a ring R right almost I-semiregular for an ideal I of R if for any a∈ R,
there exists a left R-module decomposition lRrR (a)= P⊕ Q such that P⊆ Ra and Q∩ Ra⊆ …