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This text brings the reader to the frontiers of current research in topological rings. The exercises illustrate many results and theorems while a comprehensive bibliography is also included. The book is aimed at those readers acquainted with some very basic point-set topology and algebra, as normally presented in semester courses at the beginning graduate level or even at the advanced undergraduate level. Familiarity with Hausdorff, metric, compact and locally compact spaces and basic properties of continuous functions, also with groups, rings, fields, vector spaces and modules, and with Zor
Topological rings. --- Rings, Topological --- Associative rings --- Commutative rings
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A broad range of topics is covered here, including commutative monoid rings, the Jacobson radical of semigroup rings, blocks of modular group algebras, nilpotency index of the radical of group algebras, the isomorphism problem for group rings, inverse semigroup algebras and the Picard group of an abelian group ring. The survey lectures provide an up-to-date account of the current state of the subject and form a comprehensive introduction for intending researchers.
Group rings --- Semigroup rings --- Congresses
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Graded Ring Theory
Ordered algebraic structures --- Graded rings. --- Noncommutative rings. --- Graded rings --- Noncommutative rings --- 512.55 --- Rings (Algebra) --- 512.55 Rings and modules --- Rings and modules --- Non-commutative rings --- Associative rings
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Rings That are Nearly Associative
Associative rings. --- Rings (Algebra) --- Algebraic rings --- Ring theory --- Algebraic fields
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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
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