Algebras, Rings and Modules, Volume 2 Non-commutative Algebras and Rings PDF

Features

Elucidates the structure of many classes of non-commutative and non-Noetherian rings, such as hereditary and semi-hereditary rings, distributive and semi-distributive rings, serial non-singular rings, and others. Discusses the basic concepts of projective, injective, and weak dimension of modules and the recent results on the classification of rings from the homological point of view. Contains the basic concepts and recent results on the representation theory of Artinian and semi-perfect rings. Describes modules over semi-perfect rings in terms of ‘matrix problems’ and presents the solution of mixed matrix problems over discrete valuation rings and division rings.

Summary

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This is the second volume of Algebras, Rings and Modules: Non-commutative Algebras and Rings by M. Hazewinkel and N. Gubarenis, a continuation stressing the more important recent results on advanced topics of the structural theory of associative algebras, rings and modules.

Authors: Michiel Hazewinkel, Nadiya M. Gubareni