Strongly clean matrix rings over local rings
Strongly clean matrix rings over local rings
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DOI：
10.1016/j.jalgebra.2006.10.032
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发表时间：
2007-06
影响因子：
0.9
通讯作者：
Yuanlin Li
中科院分区：
文献类型：
--
作者：
Yuanlin Li
有单位元的环R的一个元素称为强干净，如果它是一个幂等元和一个交换单位的和，如果R的每个元素都是强干净的，则R称为强干净的。在本文中，我们确定了交换局部环上的2×2矩阵A何时是强清洁的。给出了这种矩阵强清洁的几个等价判据。因此，我们得到了交换局部环上的2×2矩阵环是强清洁的几个等价条件，推广了Chen，Yang和周的一个结果。
An element of a ring R with identity is called strongly clean if it is the sum of an idempotent and a unit that commute, and R is called strongly clean if every element of R is strongly clean. In this paper, we determine when a 2×2 matrix A over a commutative local ring is strongly clean. Several equivalent criteria are given for such a matrix to be strongly clean. Consequently, we obtain several equivalent conditions for the 2×2 matrix ring over a commutative local ring to be strongly clean, extending a result of Chen, Yang, and Zhou.