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arXiv · 2204.12234

{\Sigma}-dual Rickart modules

Shiv Kumar·Ashok Ji Gupta
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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

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Shiv Kumar, Ashok Ji Gupta. 2022-04-26. {\Sigma}-dual Rickart modules. https://arxiv.org/abs/2204.12234

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