This book contains the definitions of several ring constructions used in various applications. The concept of a groupoid-graded ring includes many of these constructions as special cases and makes it possible to unify the exposition. Recent research results on groupoid-graded rings and more specialized constructions are presented. In addition, there is a chapter containing open problems currently considered in the literature.Ring Constructions and Applications can serve as an excellent introduction for graduate students to many ring constructions as well as to essential basic concepts of group, semigroup and ring theories used in proofs.
Preliminaries; Graded Rings; Examples of Ring Constructions; The Jacobson Radical; Groups of Units; Finiteness Conditions; Pl-Rings and Varieties; Gradings of Matrix Rings; Examples of Applications; Open Problems.