Semiclean Rings
Semiclean Rings
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DOI：
10.1081/agb-120023977
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发表时间：
2003-01
影响因子：
0.7
通讯作者：
Y. Ye
中科院分区：
文献类型：
--
作者：
Y. Ye
定义了环中半纯元素的概念。每一个干净的元素都是半干净的。如果环R中的每个元素都是半干净的，则称环R是半干净的。证明了具有3阶环的群环zpg是半净的。n × n矩阵环mn (R)在半干净环上是半干净的。如果R是一个无扭转的半干净环，其中R的每个元素都可以写成周期和±1的和，那么R是干净的。具有2可逆的半净环R中的每个元素是不超过3个单位的和。
Abstract The notion of semiclean elements in a ring is defined. Every clean element is semiclean. A ring R is said to be semiclean if every element in R is semiclean. The group ring Z p G with G a cyclic group of order 3 is proved to be semiclean. The n × n matrix ring M n (R) over a semiclean ring is semiclean. If R is a torsion free semiclean ring in which every element of R can be written as a sum of periodic and ±1, then R is clean. Every element in a semiclean ring R with 2 invertible is a sum of no more than 3 units.