交换局部环上强J-clean矩阵（英文）  

Strongly J-clean Matrices Over Commutative Local Rings

作　　者：陈焕银[1] CHEN Huanyin(Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang, 310036, P. R)

机构地区：[1]杭州师范大学理学院,杭州浙江310036

出　　处：《数学进展》2017年第2期212-220,共9页Advances in Mathematics（China）

基　　金：Supported by the Natural Science Foundation of Zhejiang Province(No.LY17A010018)

摘　　要：环中元素称为强J-clean,如果它可写成幂等元与其Jacobson根中元素之和,并且它们可交换.本文研究了交换局部环上强J-clean 2×2矩阵,进而确定了素数p生成的素理想的局部化环Z_(p)和p-adic整数环Z_p上强J-clean 2×2矩阵.An element of a ring is called strongly J-clean provided that it can be written as the sum of an idempotent and an element in its Jacobson radical that commute. In this paper, we investigate a single strongly J-clean 2 × 2 matrix over a commutative local ring. As consequences, the strongly J-clean 2 × 2 matrices over the localization of Z at the prime ideal generated by a prime number p and the ring Z^p of p-adic integers are completely determined.

关 键 词：2×2矩阵 强J-clean性 交换局部环 

分 类 号：O153.3[理学—数学]