Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 164, Pages 3–73 (Mi into458)  
Arithmetical rings

A. A. Tuganbaevab

a Lomonosov Moscow State University
b National Research University "Moscow Power Engineering Institute"
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Abstract: In this paper, some familiar and new results on arithmetical rings, modules, and Besout rings (not necessarily commutative) are provided. In particular, we examine relationships between arithmetical rings and their localizations by maximal ideals, saturated submodules and saturations, localizable rings, properties of annihilators of finitely generated modules over arithmetical rings, diagonalizable rings, rings with flat right ideals, and rings with quasi-projective finitely generated right ideals, Hermite rings, Pierce stalks, and rings with Krull dimension.
Keywords: arithmetic ring, distribution module, flat module, localization by maximal ideal, Bezout ring, Hermite ring, diagonalizable ring, Pierce stalk.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00452-А
Russian Science Foundation 16-11-10013
This work was supported by the Russian Foundation for Basic Research (project No. 14-01-00452-А) and the Russian Science Foundation (project No. 16-11-10013).
Bibliographic databases:
Document Type: Article
UDC: 512.55
MSC: 16Dxx, 13Fxx, 16Exx, 16Pxx
Language: Russian
Citation: A. A. Tuganbaev, “Arithmetical rings”, Algebra, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 164, VINITI, Moscow, 2019, 3–73
Citation in format AMSBIB
\Bibitem{Tug19}
\by A.~A.~Tuganbaev
\paper Arithmetical rings
\inbook Algebra
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 164
\pages 3--73
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into458}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4014982}
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