Distributive modules and rings and their close analogs (Q1291183)

This work contains a detailed and rather complete survey of results on distributive rings and modules, and also on connections of distributivity with many other well-known properties. The theorems are supplied with short proofs or indications on them. A very wide spectrum of themes and questions is developed, that is evident from the enumeration of some sections: uniserial modules and rings, Bézout modules, right Prüfer rings, Noetherian rings, endomorphism rings, classical and maximal rings of fractions, flat and projective ideals, regular and spectral modules, etc. For every type of rings or modules studied conditions are indicated which are equivalent to the distributivity (sometimes in combination with other conditions). Some deep and interesting relationships are found for various classes of rings and modules, and also for such constructions as rings of quotients and rings of endomorphisms, for diverse generalizations of projectivity and injectivity. An essentially broadened and supplemented variant of this work was published as a monograph of the series ``Mathematics and its applications'', Vol. 449 [\textit{A. A. Tuganbaev}, ``Semidistributive modules and rings'', Kluwer Academic Publishers (1998; Zbl 0909.16001)].