On $J$-rigid rings

Authors : Soraya KARİMİ, Shervin SAHEBİ, Mohammad HABİBİ

Pages : 1815-1823

Doi:10.15672/HJMS.2018.646

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Publication Date : 2019-12-08

Article Type : Research Paper

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