Unit Groups of Classical Rings

By Gregory Karpilovsky

The purpose of this book is to give a self-contained, up-to-date account of the structure of unit groups of classical rings. In so doing, the work draws together four areas of mathematics: ring theory, group theory, group representation theory, and algebraic number theory. The ensuing interplay between these disciplines provides a unique source of enrichment for each of them. The main theme centers on two related problems: to determine the isomorphism class of the unit group (U)R of ring R in terms of natural invariants associated with R; and to find an effective method for the construction of units of ring R. Various threads of the development are tied together to convey a comprehensive picture of the current state of the subject. Examples are provided to help research workers who need 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. The text is distinguished by its very clear exposition.

• Format: Hardcover
• Language: English
• ISBN: 0198535570
• ISBN13: 9780198535577
• Release Date: November 1988
• Publisher: Oxford University Press, USA
• Length: 384 Pages
• Weight: 1.58 lbs.
• Dimensions: 1.0" x 6.3" x 9.5"