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Algebra and Discrete Mathematics, 2015, Volume 20, Issue 2, Pages 317–324 (Mi adm546)  
RESEARCH ARTICLE

Quasi-Euclidean duo rings with elementary reduction of matrices

O. Romaniv, A. Sagan

Department of Mechanics and Mathematics, Ivan Franko National University of L'viv
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Abstract: We establish necessary and sufficient conditions under which a class of quasi-Euclidean duo rings coincides with a class of rings with elementary reduction of matrices. We prove that a Bezout duo ring with stable range 1 is a ring with elementary reduction of matrices. It is proved that a semiexchange quasi-duo Bezout ring is a ring with elementary reduction of matrices iff it is a duo ring.
Keywords: Bezout ring, duo ring, stable range, semiexchange ring, ring with elementary reduction of matrices.
Received: 17.11.2015
Revised: 17.11.2015
Bibliographic databases:
Document Type: Article
MSC: 13F99
Language: English
Citation: O. Romaniv, A. Sagan, “Quasi-Euclidean duo rings with elementary reduction of matrices”, Algebra Discrete Math., 20:2 (2015), 317–324
Citation in format AMSBIB
\Bibitem{RomSag15}
\by O.~Romaniv, A.~Sagan
\paper Quasi-Euclidean duo rings with elementary reduction of matrices
\jour Algebra Discrete Math.
\yr 2015
\vol 20
\issue 2
\pages 317--324
\mathnet{http://mi.mathnet.ru/adm546}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3453820}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000378729300009}
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