SEMICLEAN RINGS AND RINGS OF CONTINUOUS FUNCTIONS

被引：11

作者：

Arora, Nitin ^{[1
]}

Kundu, S. ^{[1
]}

机构：

[1] Indian Inst Technol, Dept Math, Delhi 110016, India

来源：

JOURNAL OF COMMUTATIVE ALGEBRA | 2014年 / 6卷 / 01期

关键词：

Clean rings; Semiclean; Weakly clean; Rings of continuous functions; CLEAN RINGS; UNIT;

D O I：

10.1216/JCA-2014-6-1-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

As defined by Ye [12], a ring is semiclean if every element is the sum of a unit and a periodic element. Ahn and Anderson [1] called a ring weakly clean if every element can be written as u + e or u - e, where u is a unit and e an idempotent. A weakly clean ring is semiclean. We show the existence of semiclean rings that are not weakly clean. Every semiclean ring is 2-clean. New classes of semiclean subrings of R and C are introduced and conditions are given when these rings are clean. Cleanliness and related properties of C(X, A) are studied when A is a dense semiclean subring of R or C.

引用

页码：1 / 16

页数：16

共 12 条

[1] Weakly clean rings and almost clean rings [J].