Radical Theory of Rings

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ISBN 9780824750336
Cat# DK2930



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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.

    Editorial Reviews

    "This excellent and conceptually self-contained book, masterfully written by the best experts in radical theory, reflects the present state of the field and gives a clear picture of research in the theory of radicals. … [T]his book brings together in a coherent and a comprehensive fashion the most important and up-to-date material on radical theory previously scattered in the literature. Some of this material was either not available or not easily accessible in the West before. The authors deserve our thanks for bringing it to a wide audience. The wealth of material in the book is enormous. The exposition is elegant and clear. … It is an indispensable reference book for a researcher in ring theory and is also an ideal source book for a 'topic' graduate course or a student seminar."
    - Zentralblatt MATH

    "In 1988, L. Marki, R. Mlitz and R. Wiegandt presented an axiomatic unified approach to radical theory which includes all known special types of radicals in universal classes of 'ring-like' objects. This approach is the starting-point of the book, which provides a rather full account on the subject, in particular of the developments in the last 30 years. … All in all a very recommendable monograph on this central topic!"
    - Monatshefte fur Mathematik