ON A THEOREM OF ANDERSON AND CHUN

被引:0
作者
Aliabad, Ali Rezaie [1 ]
Farrokhpay, Farimah [1 ]
Siavoshi, Mohammad Ali [1 ]
机构
[1] Shahid Chamran Univ Ahvaz, Dept Math, Ahvaz, Iran
关键词
RINGS; IDEALS; C(X);
D O I
10.1216/rmj.2023.53.1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A commutative ring R is called strongly regular associate if, for any a, b ? R, Ra = Rb implies that a = rb and sa = b for some regular elements r, s E R. In this paper, we first give a characterization of strongly regular associate rings. A ring R is said to have regular range 1 if, for any a, b ? R, Ra + Rb = R implies that a + bx is a regular for some x E R. We show that the ring of continuous functions C(X) is strongly regular associate if and only if it has regular range 1. Finally, we generalize a theorem of Anderson and Chun, which states that C([a, b]) is a strongly regular associate ring.
引用
收藏
页码:1 / 9
页数:9
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