Semidistributive modules
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.
scientific article; zbMATH DE number 1364733
scientific article