交换局部环上强J-clean矩阵

摘要

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 Zp of p-adic integers are completely determined.%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Zp上强J-clean 2×2矩阵.