Dedekind-Finite Strongly Clean Rings

Victor Camillo; Thomas J Dorsey; Pace P Nielsen

doi:10.1080/00927872.2012.746976

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Journal article

Peer reviewed

Dedekind-Finite Strongly Clean Rings

Victor Camillo, Thomas J Dorsey and Pace P Nielsen

Communications in Algebra, Vol.42(4), pp.1619-1629

04/03/2014

DOI: 10.1080/00927872.2012.746976

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Abstract

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.

Primary 16E50

Strongly clean ring

Dedekind-finite

Secondary 16D50, 16D70

Details

Title: Subtitle: Dedekind-Finite Strongly Clean Rings
Creators: Victor Camillo - Department of Mathematics , University of Iowa
Thomas J Dorsey - Center for Communications Research
Pace P Nielsen - Department of Mathematics , Brigham Young University
Resource Type: Journal article
Publication Details: Communications in Algebra, Vol.42(4), pp.1619-1629
DOI: 10.1080/00927872.2012.746976
ISSN: 0092-7872
eISSN: 1532-4125
Publisher: Taylor & Francis Group
Language: English
Date published: 04/03/2014
Academic Unit: Mathematics
Record Identifier: 9983985821902771

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