Radical Theory of Rings

1st Edition

J.W. Gardner, R. Wiegandt

CRC Press
Published November 19, 2003
Reference - 408 Pages
ISBN 9780824750336 - CAT# DK2930
Series: Chapman & Hall/CRC Pure and Applied Mathematics


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  • Provides a systematic treatment of the theory of Kurosh-Amitsur radicals as well as of concrete radicals of associative rings
  • Delves into hereditary, supernilpotent, special, supplementing, normal, subidempotent, and A-radicals
  • Introduces concrete radicals as examples of the general theory
  • Arrives at the study of nil radicals and Jacobson, Brown-McCoy, Behrens, antisimple, strongly prime, and generalized nil radicals
  • Discusses in detail Density Theorem, Wedderburn-Artin Theorems, and Litoff-Anh Theorem
  • Examines the radicals of matrix and polynomial rings and their connection with Koethe's Problem
  • Offers full proofs for theorems
  • Summary

    Radical Theory of Rings distills the most noteworthy present-day theoretical topics, gives a unified account of the classical structure theorems for rings, and deepens understanding of key aspects of ring theory via ring and radical constructions. Assimilating radical theory's evolution in the decades since the last major work on rings and radicals was published, the authors deal with some distinctive features of the radical theory of nonassociative rings, associative rings with involution, and near-rings. Written in clear algebraic terms by globally acknowledged authorities, the presentation includes more than 500 landmark and up-to-date references providing direction for further research.