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 …

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 …

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 homo-uniserial modules and rings as a nontrivial
generalization of homo-uniserial modules and rings. An R-module M is virtually homo …

This article is a sequel to the recent three papers on “virtually semisimple modules and
rings,” by Behboodi et al., which two of them appeared in the Algebras and Representation …

We define prime uniserial modules as a generalization of uniserial modules. We say that an
R-module M is prime uniserial (℘-uniserial) if its prime submodules are linearly ordered by …

In this paper, we study rings with the property that every cyclic module is almost-injective
(CAI). It is shown that R is an Artinian serial ring with J (R)^ 2= 0 J (R) 2= 0 if and only if R is …

Recall that a module M is called distributive if K∩(L+ N)= K∩ L+ K∩ N for any submodules
K, L, N. Clearly, submodules and quotient modules of a distributive module are distributive …

A result of Nakayama and Skornyakov states that a ring R is an Artinian serial ring if and
only if every R-module is serial. This motivated us to study commutative rings for which every …

We introduce and study a nontrivial generalization of uniserial modules and rings. A module
is called weakly uniserial if its submodules are comparable regarding embedding. Also, a …