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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 2, Pages 239–254
DOI: https://doi.org/10.33048/smzh.2020.61.201 (Mi smj5978) 		 
Rings whose every right ideal is a finite direct sum of automorphism-invariant right ideals

A. N. Abyzova, T. H. Phanb, C. Q. Truongc

a Kazan (Volga Region) Federal University
b Ton Duc Thang University, Ho Chi Minh City, Vietnam
c The University of Danang
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DOI: https://doi.org/10.33048/smzh.2020.61.201
Abstract: We study the rings $R$ whose every right ideal is a finite direct sum of automorphism-invariant right $R$-modules. These rings are called right $\Sigma$-$a$-rings. We find a representation in the form of block upper triangular rings of formal matrices for the indecomposable right Artinian right hereditary right $\Sigma$-$a$-rings.
Keywords: automorphism-invariant module, $\Sigma$-$a$-ring, regular ring, hereditary Artinian ring, serial ring.
Funding agency Grant number
National Foundation for Science and Technology Development Vietnam 101.04-2017.22
Russian Foundation for Basic Research 18-41-160024
C. Q. Truong and T. H. Phan were supported by the Vietnam National Foundation for Science and Technology Development (Grant 101.04-2017.22). A. N. Abyzov was supported by the Russian Foundation for Basic Research and the Government of the Republic of Tatarstan (Grant 18–41–160024).
Received: 03.08.2019
Revised: 12.09.2019
Accepted: 18.10.2019
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 2, Pages 187–198
DOI: https://doi.org/10.1134/S0037446620020019
Bibliographic databases:
Document Type: Article
UDC: 512.55
MSC: 35R30
Language: Russian
Citation: A. N. Abyzov, T. H. Phan, C. Q. Truong, “Rings whose every right ideal is a finite direct sum of automorphism-invariant right ideals”, Sibirsk. Mat. Zh., 61:2 (2020), 239–254; Siberian Math. J., 61:2 (2020), 187–198
Citation in format AMSBIB
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