Unit Groups of Classical Rings - Tapa dura

Sinopsis

This book draws together four areas of mathematics - ring theory, group theory, group representation theory and algebraic number theory, examining their interplay. The main theme centres on two related problems: Problem A - given a ring R, determine the isomorphism class of the unit group [U]R of R in terms of natural invariants associated with R. Problem B - given a ring R, find an effective method for the construction of units of R. The study aims to convey a comprehensive picture of the current state of the subject. Examples have been included to help the research worker who needs to compute explicitly unit groups of certain rings. A familiarity with basic ring-theoretic and group-theoretic concepts is assumed, but a chapter on algebraic preliminaries is included.

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