Symmetricity of rings relative to the prime radical
In this paper, we introduce and study a strict generalization of symmetric rings. We call a ring $R$ \textit{`$P$-symmetric' } if for any $a,\, b,\, c\in R,\, abc=0$ implies $bac\in P(R)$, where $P(R)$ is the prime radical of $R$. It is shown that the class of $P$-symmetric rings lies between...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2022-12-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/51713 |
| Summary: | In this paper, we introduce and study a strict generalization of symmetric rings. We call a ring $R$ \textit{`$P$-symmetric' } if for any $a,\, b,\, c\in R,\, abc=0$ implies $bac\in P(R)$, where $P(R)$ is the prime radical of $R$. It is shown that the class of $P$-symmetric rings lies between the class of central symmetric rings and generalized weakly symmetric rings. Relations are provided between $P$-symmetric rings and some other known classes of rings. From an arbitrary $P$-symmetric ring, we produce many families of $P$-symmetric rings.
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| ISSN: | 0037-8712 2175-1188 |