Arithmetical Rings

In this paper, some familiar and new results on arithmetical rings, modules, and Bezout 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 ri...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2021-10, Vol.258 (2), p.129-198
Main Author: Tuganbaev, A. A.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Modules
Rings (mathematics)
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Summary:In this paper, some familiar and new results on arithmetical rings, modules, and Bezout 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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05541-w