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Although the main difficulties can already be handled for prime rings, it is not always possible to transfer proofs directly to the case of semiprime rings. Very often one has to repeat the same arguments in different situations. This phenomena brought about the proof of a metatheorem stating that many results expressed in the language of mathematical logic can be automatically transferred from the class of prime rings to a large class of semiprime rings.

The book is organized as follows. Chapter 1 is introductory. It is devoted to the Baer radical in the structure theory of rings, the Bergman-Isaacs theorem for the nilpotency of rings with a fixed-point-free group action, the Quinn theorem on integrality over fixed subrings, the Martindale theorem for rings with generalized identities and the metatheorem.

Chapter 2 deals with the algebraic independence of automorphisms and derivations of semiprime rings. More precisely, it turns out that all algebraic dependences are consequences of the obvious ones, which define the algebraic structure of the sets of automorphisms and derivations. The next three chapters are devoted to Galois theory for automorphisms and derivations, first in the class of prime rings and then, by metatheorem, in the class of semiprime rings.

The final chapter contains applications to free associative algebras, the finite generation of the algebra of noncommutative invariants with additional action of symmetric groups, Montgomery equivalence, Hopf algebra actions. A good list of references is given as well. K Kharchenko Book 1 edition published in in Russian and held by 2 WorldCat member libraries worldwide.

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