STRONGLY CLEAN TRIANGULAR MATRIX RINGS WITH ENDOMORPHISMS

被引：0

作者：

Chen, H. ^{[1
]}

Kose, H. ^{[2
]}

Kurtulmaz, Y. ^{[3
]}

机构：

[1] Hangzhou Normal Univ, Dept Math, Hangzhou 310034, Zhejiang, Peoples R China

[2] Ahi Evran Univ, Dept Math, Kirsehir, Turkey

[3] Bilkent Univ, Dept Math, Ankara, Turkey

来源：

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY | 2015年 / 41卷 / 06期

关键词：

Strongly clean rings; skew triangular matrix rings; local rings;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A ring R is strongly clean provided that every element in R is the sum of an idempotent and a unit that commutate. Let T-n(R, sigma) be the skew triangular matrix ring over a local ring R where a is an endomorphism of R. We show that T-2(R, sigma) is strongly clean if and only if for any a is an element of 1 + J(R),b is an element of J(R), l(a) - r(sigma(b)) : R -> R is surjective. Further, T-3(R, sigma) is strongly clean if l(a) - r(sigma(b)), l(a) - r(sigma 2(b)) and l(b) - r(sigma(a)) are surjective for any a is an element of U(R), b is an element of J(R). The necessary condition for T-3(R, sigma) to be strongly clean is also obtained.

引用

页码：1365 / 1374

页数：10