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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Veröffentlicht in:	Journal of mathematical sciences (New York, N.Y.) N.Y.), 2021-10, Vol.258 (2), p.129-198
1. Verfasser:	Tuganbaev, A. A.
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics Mathematics and Statistics Modules Rings (mathematics)
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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