Extensions and topological conditions of NJ rings

Authors

MEIMEI JIANG
YAO WANG
YANLI REN

DOI

10.3906/mat-1805-103

Abstract

A ring $R$ is said to be NJ if $J(R)=N(R)$. This paper mainly studies the relationship between NJ rings and related rings, and investigates the Dorroh extension, the Nagata extension, the Jordan extension, and some other extensions of NJ rings. At the same time, we also prove that if $R$ is a weakly 2-primal $\alpha$-compatible ring with an isomorphism $\alpha$ of $R$, then $R[x;\alpha]$ is NJ; if $R$ is a weakly 2-primal $\delta$-compatible ring with a derivation $\delta$ of $R$, then $R[x;\delta]$ is NJ. Moreover, we consider some topological conditions for NJ rings and show for a NJ ring $R$ that $R$ is J-pm if and only if $J$-$Spec(R)$ is a normal space if and only if $Max(R)$ is a retract of $J$-$Spec(R)$.

Keywords

Jacobson radical, nilpotent element, weakly 2-primal ring, polynomial extension, topological space

First Page

44

Last Page

62

Recommended Citation

JIANG, MEIMEI; WANG, YAO; and REN, YANLI (2019) "Extensions and topological conditions of NJ rings," Turkish Journal of Mathematics: Vol. 43: No. 1, Article 5. https://doi.org/10.3906/mat-1805-103
Available at: https://journals.tubitak.gov.tr/math/vol43/iss1/5