On modules whose coclosed submodules are isomorphic to direct summands
LK Das, MK Patel - Proceedings of the Indian National Science Academy, 2022 - Springer
Inspired by the notion of virtually extending module, in this work we have proposed and
investigated the behaviours of virtually lifting module as the dual of virtually extending …
investigated the behaviours of virtually lifting module as the dual of virtually extending …
Virtually regular modules
E Büyükaşık, ÖI Demir - arXiv preprint arXiv:2406.11222, 2024 - arxiv.org
We call a right module $ M $(strongly) virtually regular if every (finitely generated) cyclic
submodule is isomorphic to a direct summand. $ M $ is said to be completely virtually …
submodule is isomorphic to a direct summand. $ M $ is said to be completely virtually …
Direct sum decompositions of projective and injective modules into virtually uniserial modules
M Behboodi, A Moradzadeh-Dehkordi… - Revista de la Real …, 2022 - Springer
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 …
generated) projective left R-module is serial” and a theorem due to Tuganbaev states that “a …
A generalization of uniserial modules and rings
S Shirzadi, R Beyranvand… - arXiv preprint arXiv …, 2023 - arxiv.org
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 …
is called weakly uniserial if its submodules are comparable regarding embedding. Also, a …
Virtually homo-uniserial modules and rings
M Behboodi, A Moradzadeh-Dehkordi… - Communications in …, 2021 - Taylor & Francis
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 …
generalization of homo-uniserial modules and rings. An R-module M is virtually homo …
Cyclic-Uniform Uniserial Modules and Rings
R Nikandish, MJ Nikmehr, A Yassine - arXiv preprint arXiv:2208.07940, 2022 - arxiv.org
An $ R $-module $ M $ is called virtually uniserial if for every finitely generated submodule
$0\neq K\subseteq M $, $ K/$ Rad $(K) $ is virtually simple. In this paper, we generalize …
$0\neq K\subseteq M $, $ K/$ Rad $(K) $ is virtually simple. In this paper, we generalize …