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.
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