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Rings That are Nearly Associative
Associative rings. --- Rings (Algebra) --- Algebraic rings --- Ring theory --- Algebraic fields
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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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Commutative rings --- Group rings --- Unit groups (Ring theory)
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Algebra --- Algebra. --- Mathematical Sciences --- Applied Mathematics --- algebra --- modules --- ring theory --- homology
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Ring theory
Rings (Algebra) --- Associative rings. --- Algebraic rings --- Ring theory --- Algebraic fields --- Algèbres associatives --- Algèbres non associatives
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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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This study of graded rings includes the first systematic account of the graded Grothendieck group, a powerful and crucial invariant in algebra which has recently been adopted to classify the Leavitt path algebras. The book begins with a concise introduction to the theory of graded rings and then focuses in more detail on Grothendieck groups, Morita theory, Picard groups and K-theory. The author extends known results in the ungraded case to the graded setting and gathers together important results which are currently scattered throughout the literature. The book is suitable for advanced undergraduate and graduate students, as well as researchers in ring theory.
Grothendieck groups. --- Graded rings. --- Rings (Algebra) --- Algebraic rings --- Ring theory --- Algebraic fields --- Group theory
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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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512.55 --- Rings and modules --- 512.55 Rings and modules --- Unit groups (Ring theory). --- Associative rings. --- Rings (Algebra)
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RINGS (Algebra) --- Factorization (Mathematics) --- Rings (Algebra). --- Factorization (Mathematics). --- Rings (Algebra) --- Algebraic rings --- Ring theory --- Algebraic fields --- Mathematics --- Algebra
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