A Property Satisfying Reducedness over Centers  

作　　者：Hailan Jin Tai Keun Kwak Yang Lee Zhelin Piao 

机构地区：[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

出　　处：《Algebra Colloquium》2021年第3期453-468,共16页代数集刊（英文版）

基　　金：The second author was supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(No.2019R1F1A1040405).

摘　　要：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 R,it is proved that if R is pseudo-reduced-over-center,then R is commutative and R/J(R)is a commutative regular ring with J(R)nil,where J(R)is the Jacobson radical of R.

关 键 词：pseudo-reduced-over-center ring CENTER RADICAL commutative ring polynomial ring right quotient ring Abelian ring 

分 类 号：O17[理学—数学]