Topological Rings Satisfying Compactness Conditions: 549 (Mathematics and Its Applications, 549) - Hardcover
Synopsis
Focusing mainly on locally compact and compact rings, the text begins by illustrating results from the theory of topological groups, some of which are very recent results published for the first time. Constructions and examples of topological groups, relations between quasi-components and components in topological groups, minimal topological groups and properties of the finest precompact topology on an Abelian group are all covered. The text then goes on to examine various aspects of the theory of topological rings, covering constructions and examples of compact right topological rings, the local structure of locally compact rings, structure of compact rings, the local nilpotence of nilrings satisfying compactness conditions, groups of units of compact rings, bounded locally compact rings, topologically locally finite and locally topologically nilpotent radicals in the class of locally compact rings, rings of endomorphisms of a locally compact module and tensor products of compact rings. Results on totally bounded topological rings are also given and developed e.g. the structure theory for countably compact rings. This book will be invaluable to researchers and mathematicians with a basic grounding in the theory of rings and general topology.
"synopsis" may belong to another edition of this title.
Synopsis
The main aim of this text is to introduce the beginner to the theory of topological rings. Whilst covering all the essential theory of topological groups, the text focuses on locally compact, compact, linearly compact, hereditarily linear compact and bounded topological rings. The text also contains new, unpublished results on topological rings, for example the nilideals of topological rings, trivial extensions of special type, rings with a unique compact topology, compact right topological rings and the results from groups of units of topological rings.
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Topological Rings Satisfying Compactness Conditions (Mathematics and Its Applications, 549)
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Topological Rings Satisfying Compactness Conditions
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Introduction In the last few years a few monographs dedicated to the theory of topolog ical rings have appeared [Warn27], [Warn26], [Wies 19], [Wies 20], [ArnGM]. Ring theory can be viewed as a particular case of Z-algebras. Many general results true for rings can be extended to algebras over commutative rings. In topological algebra the structure theory for two classes of topological algebras is well developed: Banach algebras; and locally compact rings. The theory of Banach algebras uses results of Banach spaces, and the theory of locally compact rings uses the theory of LCA groups. As far as the author knows, the first papers on the theory of locally compact rings were [Pontr1]' [J1], [J2], [JT], [An], lOt], [K1]' [K2]' [K3], [K4], [K5], [K6]. Later two papers, [GS1,GS2]appeared, which contain many results concerning locally compact rings. This book can be used in two w.ays. It contains all necessary elementary results from the theory of topological groups and rings. In order to read these parts of the book the reader needs to know only elementary facts from the theories of groups, rings, modules, topology. The book consists of two parts. 342 pp. Englisch. Seller Inventory # 9781402009396
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Topological Rings Satisfying Compactness Conditions
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Hardback. Condition: New. 2002 ed. Focusing mainly on locally compact and compact rings, the text begins by illustrating results from the theory of topological groups, some of which are very recent results published for the first time. Constructions and examples of topological groups, relations between quasi-components and components in topological groups, minimal topological groups and properties of the finest precompact topology on an Abelian group are all covered. The text then goes on to examine various aspects of the theory of topological rings, covering constructions and examples of compact right topological rings, the local structure of locally compact rings, structure of compact rings, the local nilpotence of nilrings satisfying compactness conditions, groups of units of compact rings, bounded locally compact rings, topologically locally finite and locally topologically nilpotent radicals in the class of locally compact rings, rings of endomorphisms of a locally compact module and tensor products of compact rings. Results on totally bounded topological rings are also given and developed e.g. the structure theory for countably compact rings.This book will be invaluable to researchers and mathematicians with a basic grounding in the theory of rings and general topology. Seller Inventory # LU-9781402009396
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Buch. Condition: Neu. Topological Rings Satisfying Compactness Conditions | M. Ursul | Buch | ix | Englisch | 2002 | Springer Netherland | EAN 9781402009396 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. Seller Inventory # 102787160