Generalizations of almost prime and right $S$-prime ideals in noncommutative rings
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914886984925184 |
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| author | Abouhalaka, Alaa Findik, Sehmus Groenewald, Nico |
| author_facet | Abouhalaka, Alaa Findik, Sehmus Groenewald, Nico |
| contents | Let $R$ be a noncommutative ring, and let $S$ be an $m$-system of $R$. In this paper, we give more results on the concept of almost prime (right) ideals, that were introduced by the first two authors, especially in (right) $S$-unital rings, local rings, and decomposable rings. In addition, we introduce the concept of almost right $S$-prime ideals, and we show how some findings regarding almost prime ideals can be derived as consequences of almost right $S$-prime ideals. Besides, we show how almost right $S$-prime ideals behave in related rings such as homomorphic images, quotient rings, and decomposable rings. Finally, we construct almost right $S$-prime ideals using the Nagata method of idealization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_04886 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Generalizations of almost prime and right $S$-prime ideals in noncommutative rings Abouhalaka, Alaa Findik, Sehmus Groenewald, Nico Rings and Algebras Commutative Algebra 16N60, 16W99 Let $R$ be a noncommutative ring, and let $S$ be an $m$-system of $R$. In this paper, we give more results on the concept of almost prime (right) ideals, that were introduced by the first two authors, especially in (right) $S$-unital rings, local rings, and decomposable rings. In addition, we introduce the concept of almost right $S$-prime ideals, and we show how some findings regarding almost prime ideals can be derived as consequences of almost right $S$-prime ideals. Besides, we show how almost right $S$-prime ideals behave in related rings such as homomorphic images, quotient rings, and decomposable rings. Finally, we construct almost right $S$-prime ideals using the Nagata method of idealization. |
| title | Generalizations of almost prime and right $S$-prime ideals in noncommutative rings |
| topic | Rings and Algebras Commutative Algebra 16N60, 16W99 |
| url | https://arxiv.org/abs/2204.04886 |