An Extension of Semicommutative Rings via Reflexivity
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914657168523264 |
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| author | Subba, Sanjiv Subedi, Tikaram |
| author_facet | Subba, Sanjiv Subedi, Tikaram |
| contents | This article introduces the notion of an NJ-reflexive ring and demonstrates that it is distinct from the concept of a reflexive ring. The class of NJ-reflexive rings contains the class of semicommutative rings, the class of left (right) quasi-duo rings, and the class of J-clean rings but is strictly larger than these classes. Additionally, the article investigates a sufficient condition for NJ-reflexive rings to be left (right) quasi-duo, as well as some conditions for NJ-reflexive rings to be reduced. It also explores extensions of NJ-reflexive rings and notes that the NJ-reflexive property may not carry over to polynomial extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16061 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Extension of Semicommutative Rings via Reflexivity Subba, Sanjiv Subedi, Tikaram Rings and Algebras 16U80, 16S34, 16S36 This article introduces the notion of an NJ-reflexive ring and demonstrates that it is distinct from the concept of a reflexive ring. The class of NJ-reflexive rings contains the class of semicommutative rings, the class of left (right) quasi-duo rings, and the class of J-clean rings but is strictly larger than these classes. Additionally, the article investigates a sufficient condition for NJ-reflexive rings to be left (right) quasi-duo, as well as some conditions for NJ-reflexive rings to be reduced. It also explores extensions of NJ-reflexive rings and notes that the NJ-reflexive property may not carry over to polynomial extensions. |
| title | An Extension of Semicommutative Rings via Reflexivity |
| topic | Rings and Algebras 16U80, 16S34, 16S36 |
| url | https://arxiv.org/abs/2401.16061 |