Monographs and textbooks in pure and applied mathematics ;
Volume Designation
196
GENERAL NOTES
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Includes index.
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
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Includes bibliographical references (pages 493-517) and index.
CONTENTS NOTE
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1. Preliminaries -- 2. Rings of Quotients -- 3. The Method of Orthogonal Completions -- 4. Primitive Rings -- 5. The Poincare-Birkhoff-Witt Theorem -- 6. Rings with Generalized Polynomial Identities -- 7. T-identities of Prime Rings -- 8. T-identities of Semiprime Rings -- 9. Applications to Lie Theory.
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SUMMARY OR ABSTRACT
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This outstanding reference discusses the latest results concerning the area of non-commutative ring theory known as the theory of generalized identities (GIs) - detailing Kharchenko's results on GIs in prime rings, Chuang's extension to anti-automorphisms, and the use of the Beidar-Mikhalev theory of orthogonal completion in the semiprime case. Providing novel proofs of existing results, Rings with Generalized Identities puts the theory of generalized identities on a rigorous basis with the use of skew group rings ... presents Beidar's determination of the generators of the T-ideal of generalized polynomial identities in (semi)prime rings ... furnishes a thorough proof of the generalized Poincare-Birkhoff-Witt theorem for (restricted) differential Lie algebras, making extensive use of the Diamond Lemma ... gives a general account of the extended centroid and rings of quotients ... covers a recent solution to a long-standing conjecture of Herstein on Lie isomorphisms ... and more.