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Diskretnaya Matematika, 2016, Volume 28, Issue 4, Pages 150–157
DOI: https://doi.org/10.4213/dm1399 (Mi dm1399) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On serial rings

A. A. Tuganbaevab

a Lomonosov Moscow State University
b National Research University "Moscow Power Engineering Institute"
Full-text PDF (438 kB) Citations (3)
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DOI: https://doi.org/10.4213/dm1399
Abstract: Let A be a ring such that all maximal indecomposable factor rings $A_i$ of $A$ are serial rings. Then every square matrix over $A$ is diagonalizable. In addition, if all the rings $A_i$ are Bezout rings, then every rectangular matrix over $A$ is diagonalizable. If $\varphi$ is an automorphism of the ring $A$, then the skew Laurent series ring $A((x,\varphi ))$ is a serial ring if and only if $A$ is a serial Artinian ring.
Keywords: serial ring, Bezout ring, diagonalizable ring, skew Laurent series ring.
Funding agency Grant number
Russian Science Foundation 16-11-10013
The study is supported by Russian Science Foundation (project no. 16-11-10013).
Received: 24.07.2016
English version:
Discrete Mathematics and Applications, 2017, Volume 27, Issue 2, Pages 131–135
DOI: https://doi.org/10.1515/dma-2017-0016
Bibliographic databases:
Document Type: Article
UDC: 512.55
Language: Russian
Citation: A. A. Tuganbaev, “On serial rings”, Diskr. Mat., 28:4 (2016), 150–157; Discrete Math. Appl., 27:2 (2017), 131–135
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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