Semidistributive modules
type: Item
instance of: scholarly article
title: Semidistributive modules
zbMATH Open document ID: 0936.16007
DOI: 10.1007/BF02365070
published in: Journal of Mathematical Sciences (New York)
publication date: 1999-11-22T00:00:00Z
review text: This article is a survey of the most important results on distributive and semidistributive rings and modules. It is closely related to previous work of that type [\textit{A. V. Mikhalev}, \textit{A. A. Tuganbaev}, J. Math. Sci., New York 93, No. 2, 149-253 (1999; Zbl 0928.16003)]. The article consists of three chapters. In the first chapter (``Basis notions'') the following subjects are discussed: local and semiperfect rings, injective hull and finite dimensional modules, nonsingular rings and modules, rings with maximum conditions, classical localizations. In the second chapter (``Distributive modules'') the main themes are: uniserial modules, countably distributive modules, Bézout modules, modules over semiperfect rings, direct summands and closed submodules of distributive modules, endomorphisms of distributive modules. The third chapter (``Semidistributive modules and rings'') contains the following paragraphs: distributive Goldie rings, distributive Noetherian rings, semidistributive modules, serial modules and rings, arithmetical rings. As in the article mentioned, the relations between distributivity and many other properties of rings and modules are shown. A large list of literature on this domain is included.
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16-02
zbMATH DE Number: 1364733
zbMATH Keywords: semidistributive rings
zbMATH Keywords: semiperfect rings
zbMATH Keywords: uniserial modules
zbMATH Keywords: distributive modules
zbMATH Keywords: Bézout modules
zbMATH Keywords: direct summands
zbMATH Keywords: endomorphisms
zbMATH Keywords: distributive Goldie rings
zbMATH Keywords: distributive Noetherian rings
zbMATH Keywords: semidistributive modules
zbMATH Keywords: serial modules
author: A. A. Tuganbaev
reviewed by: A. I. Kashu
MaRDI profile type: Publication
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Semidistributive modules (full work available at URL)
full work available at URL: https://doi.org/10.1007/bf02365070

Semidistributive modules (OpenAlex ID)
OpenAlex ID: W4211213665