A Property Satisfying Reducedness over Centers

Author:

Jin Hailan1,Kwak Tai Keun2,Lee Yang13,Piao Zhelin1

Affiliation:

1. Department of Mathematics, Yanbian University, Yanji, Jilin 133002, China

2. Department of Mathematics, Daejin University, Pocheon 11159, Korea

3. Institute of Basic Science, Daejin University, Pocheon 11159, Korea

Abstract

This article concerns a ring property called pseudo-reduced-over-center that is satisfied by free algebras over commutative reduced rings. The properties of radicals of pseudo-reduced-over-center rings are investigated, especially related to polynomial rings. It is proved that for pseudo-reduced-over-center rings of nonzero characteristic, the centers and the pseudo-reduced-over-center property are preserved through factor rings modulo nil ideals. For a locally finite ring [Formula: see text], it is proved that if [Formula: see text] is pseudo-reduced-over-center, then [Formula: see text] is commutative and [Formula: see text] is a commutative regular ring with [Formula: see text] nil, where [Formula: see text] is the Jacobson radical of [Formula: see text].

Funder

the National Research Foundation of Korea (NRF) grant funded by the Korea government

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the condition that powers preserve noncentralness;Journal of Algebra and Its Applications;2022-08-11

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