On $J$-rigid rings

Year 2019, Volume: 48 Issue: 6, 1815 - 1823, 08.12.2019

Soraya Karimi Shervin Sahebi , Mohammad Habibi

https://doi.org/10.15672/HJMS.2018.646

https://izlik.org/JA33UH27AA

Abstract

Let $R$ be a ring with an endomorphism $\sigma$. We introduce the notion of $\sigma$-$J$-rigid rings as a generalization of $\sigma$-rigid rings, and investigate its properties. It is proved that a ring $R$ is $\sigma$-$J$-rigid if and only if $R[[x;\sigma]]$ is $\bar\sigma$-$J$-rigid, while the $\sigma$-$J$-rigid property is not Morita invariant. Moreover, we prove that every ring isomorphism preserves $J$-rigid structure, and several known results are extended.

Keywords

Rigid rings , Reduced rings , Jacobson radical , $\sigma$-$J$-rigid rings , over-rings

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