Topological Rings Satisfying Compactness Conditions

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.