Σ-dual Rickart modules
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909343418417152 |
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| author | Kumar, Shiv Gupta, Ashok Ji |
| author_facet | Kumar, Shiv Gupta, Ashok Ji |
| contents | In this paper, we dualize the concept of Σ-Rickart modules as Σ-dual Rickart modules. An R-module M is said to be Σ-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 Σ-dual Rickart. We introduce the notion of strongly cogenerated modules and characterize Σ-dual Rickart modules in terms of strongly cogenerated modules. We also study some properties of Σ- 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 Σ-dual Rickart modules |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_12234 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Σ-dual Rickart modules Kumar, Shiv Gupta, Ashok Ji Rings and Algebras In this paper, we dualize the concept of Σ-Rickart modules as Σ-dual Rickart modules. An R-module M is said to be Σ-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 Σ-dual Rickart. We introduce the notion of strongly cogenerated modules and characterize Σ-dual Rickart modules in terms of strongly cogenerated modules. We also study some properties of Σ- 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 Σ-dual Rickart modules |
| title | Σ-dual Rickart modules |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2204.12234 |