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Mathematics > Rings and Algebras

arXiv:2204.12234 (math)
[Submitted on 26 Apr 2022 (v1), last revised 10 Oct 2024 (this version, v3)]

Title:Σ-dual Rickart modules

Authors: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
Subjects: Rings and Algebras (math.RA)
Cite as: arXiv:2204.12234 [math.RA]
  (or arXiv:2204.12234v3 [math.RA] for this version)
  https://doi.org/10.48550/arXiv.2204.12234

Submission history

From: Shiv Kumar [view email]
[v1] Tue, 26 Apr 2022 11:25:12 UTC (7 KB)
[v2] Wed, 17 Aug 2022 10:21:25 UTC (13 KB)
[v3] Thu, 10 Oct 2024 17:56:39 UTC (24 KB)
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