Clean general rings

被引：72

作者：

Nicholson, WK ^{[1
]}

Zhou, Y

机构：

[1] Univ Calgary, Dept Math, Calgary, AB T2N 1N4, Canada

[2] Mem Univ Newfoundland, Dept Math, St John, NF A1C 5S7, Canada

来源：

JOURNAL OF ALGEBRA | 2005年 / 291卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

clean rings; boolean rings; idempotents;

D O I：

10.1016/j.jalgebra.2005.01.020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An associative ring with unity is called clean (respectively uniquely clean) if every element is (uniquely) the sum of an idempotent and a unit. In this paper we define clean general rings (with or without a unity) and extend many of the basic results to the wider class. In particular, a clean general ring is an exchange ring in the sense of Ara. We then study the general analogue of the uniquely clean rings and their relationship to the boolean rings. Finally, we introduce semiboolean rings as a natural generalization of boolean rings. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：297 / 311

页数：15

共 13 条

[1] Extensions of exchange rings [J].

Ara, P .

JOURNAL OF ALGEBRA, 1997, 197 (02) :409-423

[2] Separative cancellation for projective modules over exchange rings [J].

Ara, P ;

Goodearl, KR ;

O'Meara, KC ;

Pardo, E .

ISRAEL JOURNAL OF MATHEMATICS, 1998, 105 (1) :105-137

[3] A characterization of unit regular rings [J].

Camillo, VP ;

Khurana, D .

COMMUNICATIONS IN ALGEBRA, 2001, 29 (05) :2293-2295

[4] EXCHANGE RINGS, UNITS AND IDEMPOTENTS [J].

CAMILLO, VP ;

YU, HP .

COMMUNICATIONS IN ALGEBRA, 1994, 22 (12) :4737-4749

[5]

Chen H., 2003, INT J MATH MATH SCI, V62, P3949, DOI DOI 10.1155/S0161171203211339

[6]

Chen H., 1999, ALGEBR REPRESENT TH, V2, P201

[7] Extensions of clean rings [J].

Han, J ;

Nicholson, NK .

COMMUNICATIONS IN ALGEBRA, 2001, 29 (06) :2589-2595

[8]

Jacobson N., 1964, AM MATH SOC C PUBL, V37

[9] Countable linear transformations are clean [J].

Nicholson, WK ;

Varadarajan, K .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (01) :61-64

[10] LIFTING IDEMPOTENTS AND EXCHANGE RINGS [J].

NICHOLSON, WK .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1977, 229 (MAY) :269-278

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