{\Sigma}-dual Rickart modules
Rings and Algebras
2024-10-11 v3
Abstract
In this paper, we dualize the concept of {\Sigma}-Rickart modules as {\Sigma}-dual Rickart modules. An R-module M is said to be {\Sigma}-dual Rickart if the direct sum of arbitrary copies of M is dual Rickart. We prove that each cohereditary module over the Noetherian ring is a {\Sigma}-dual Rickart. We introduce the notion of strongly cogenerated modules and characterize {\Sigma}-dual Rickart modules in terms of strongly cogenerated modules. We also study some properties of {\Sigma}- dual Rickart modules and find connections with semisimple Artinian ring, regular ring semi-hereditary ring and FP-injective module. Further, we study the endomorphism ring of {\Sigma}-dual Rickart modules
Cite
@article{arxiv.2204.12234,
title = {{\Sigma}-dual Rickart modules},
author = {Shiv Kumar and Ashok Ji Gupta},
journal= {arXiv preprint arXiv:2204.12234},
year = {2024}
}