Pseudopolarity of Generalized Matrix Rings over a Local Ring

作     者：Yin Xiao-bin Dou Wan Du Xian-kun 

作者机构：College of Mathematics and Computer Science Anhui Normal University 

出 版 物：《Communications in Mathematical Research》 (数学研究通讯（英文版）)

年 卷 期：2015年第31卷第3期

页      面：211-221页

核心收录：

学科分类：07[理学] 09[农学] 070104[理学-应用数学] 0903[农学-农业资源与环境] 0701[理学-数学] 090301[农学-土壤学] 

基　　金：The NSF(10871024 11326062) of China 

主　　题：pseudopolar ring local ring generalized matrix ring 

摘      要：Pseudopolar rings are closely related to strongly -regular rings, uniquelystrongly clean rings and semiregular rings. In this paper, we investigate pseudopolar-ity of generalized matrix rings Ks（R） over a local ring R. We determine the conditionsunder which elements of Ks（R） are pseudopolar. Assume that R is a local ring. It isshown that A ∈ Ks（R） is pseudopolar if and only if A is invertible or A^2 ∈ J（Ks（R））or A is similar to a diagonal matrix [ u 0 0 j ]; where lu -rj and lj-ru are injectiveand u 2 U（R） and j ∈ J（R）. Furthermore, several equivalent conditions for Ks（R）over a local ring R to be pseudopolar are obtained.