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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 concept

Rings (Algebra) --- Algebraic rings --- Ring theory --- Algebraic fields

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The algebraic theory of corner subrings introduced by Lam (as an abstraction of the properties of Peirce corners eRe of a ring R associated with an idempotent e in R) is investigated here in the context of Banach and C*-algebras. We propose a general algebraic approach which includes the notion of ranges of (completely) contractive conditional expectations on C*-algebras and on ternary rings of operators, and we investigate when topological properties are consequences of the algebraic assumpt...

Algebra. --- Rings (Algebra) --- Algebraic rings --- Ring theory --- Algebraic fields --- Mathematics --- Mathematical analysis

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The text of the first volume of the book covers the major topics in ring and module theory and includes both fundamental classical results and more recent developments. The basic tools of investigation are methods from the theory of modules, which allow a very simple and clear approach both to classical and new results. An unusual main feature of this book is the use of the technique of quivers for studying the structure of rings. A considerable part of the first volume of the book is devoted to a study of special classes of rings and algebras, such as serial rings, hereditary rings, semidistr

Rings (Algebra) --- Modules (Algebra) --- Finite number systems --- Modular systems (Algebra) --- Algebraic rings --- Ring theory --- Algebra --- Finite groups --- Algebraic fields

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Galois theory. --- Rings (Algebra) --- Algebraic rings --- Ring theory --- Algebraic fields --- Equations, Theory of --- Group theory --- Number theory

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Polynomial identities in ring theory

Ordered algebraic structures --- Polynomial rings. --- Rings (Algebra) --- Polynomial rings --- 512.55 --- 512.55 Rings and modules --- Rings and modules --- Commutative rings --- Algebraic rings --- Ring theory --- Algebraic fields