DEDEKIND-FINITE STRONGLY CLEAN RINGS

被引：4

作者：

Camillo, Victor ^{[1
]}

Dorsey, Thomas J. ^{[2
]}

Nielsen, Pace P. ^{[3
]}

机构：

[1] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

[2] Ctr Commun Res, San Diego, CA USA

[3] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

来源：

COMMUNICATIONS IN ALGEBRA | 2014年 / 42卷 / 04期

关键词：

Dedekind-finite; Strongly clean ring; Primary; 16E50; Secondary; 16D50; 16D70; 16U99; EXCHANGE;

D O I：

10.1080/00927872.2012.746976

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we partially answer two open questions concerning clean rings. First, we demonstrate that if a quasi-continuous module is strongly clean then it is Dedekind-finite. Second, we prove a partial converse. We also prove that all clean decompositions on submodules of continuous modules extend to the entire module.

引用

页码：1619 / 1629

页数：11

共 50 条

[1] A Taxonomy of Dedekind-Finite and Reflexive Rings
Szabo, Steve
[J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2023, 20 (05)
[2] A Taxonomy of Dedekind-Finite and Reflexive Rings
Steve Szabo
[J]. Mediterranean Journal of Mathematics, 2023, 20
[3] Dedekind-finite acts over monoids
Ahmadi, Kamal
Madanshekaf, Ali
[J]. COMMUNICATIONS IN ALGEBRA, 2017, 45 (01) : 377 - 383
[4] DEDEKIND-FINITE CARDINALS HAVING COUNTABLE PARTITIONS
Panasawatwong, Supakun
Truss, John Kenneth
[J]. JOURNAL OF SYMBOLIC LOGIC, 2023,
[5] The first-order structure of weakly Dedekind-finite sets
Walczak-Typke, AC
[J]. JOURNAL OF SYMBOLIC LOGIC, 2005, 70 (04) : 1161 - 1170
[6] π-Clean and strongly π-clean rings
Sabet, Sh. A. Safari
Farmani, M.
Karami, M.
[J]. MEASUREMENT, 2017, 109 : 74 - 78
[7] Strongly graded rings which are generalized Dedekind rings
Wahyuni, Sri
Marubayashi, Hidetoshi
Ernanto, Iwan
Sutopo
[J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2020, 19 (03)
[8] ON STRONGLY *-CLEAN RINGS
Li, Chunna
Zhou, Yiqiang
[J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2011, 10 (06) : 1363 - 1370
[9] On strongly nil clean rings
Chen, Huanyin
Sheibani, Marjan
[J]. COMMUNICATIONS IN ALGEBRA, 2017, 45 (04) : 1719 - 1726
[10] A NOTE ON STRONGLY *-CLEAN RINGS
Cui, Jian
Wang, Zhou
[J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2015, 52 (04) : 839 - 851

← 1 2 3 4 5 →