Symmetricity of rings relative to the prime radical

Debraj Roy; Tikaram Subedi

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arXiv · 2001.02864

Symmetricity of rings relative to the prime radical

Debraj Roy·Tikaram Subedi

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Abstract

In this paper, we introduce and study a strict generalization of symmetric rings. We call a ring $R \,\,\, 'P-symmetric'$ 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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Debraj Roy, Tikaram Subedi. 2020-01-09. Symmetricity of rings relative to the prime radical. https://arxiv.org/abs/2001.02864

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