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＜電子ブック＞
Automorphisms and Derivations of Associative Rings / by V. Kharchenko
(Mathematics and its Applications, Soviet Series ; 69)

版	1st ed. 1991.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1991
本文言語	英語
大きさ	XIV, 385 p : online resource
著者標目	*Kharchenko, V author SpringerLink (Online service)
件　名	LCSH:Commutative algebra LCSH:Commutative rings LCSH:Associative rings LCSH:Associative algebras LCSH:Nonassociative rings FREE:Commutative Rings and Algebras FREE:Associative Rings and Algebras FREE:Non-associative Rings and Algebras
一般注記	1. Structure of Rings -- 1.1 Baer Radical and Semiprimeness -- 1.2 Automorphism Groups and Lie Differential Algebras -- 1.3 Bergman-Isaacs Theorem. Shelter Integrality -- 1.4 Martindale Ring of Quotients -- 1.5 The Generalized Centroid of a Semiprime Ring -- 1.6 Modules over a Generalized Centroid -- 1.7 Extension of Automorphisms to a Ring of Quotients. Conjugation Modules -- 1.8 Extension of Derivations to a Ring of Quotients -- 1.9 The Canonical Sheaf of a Semiprime Ring -- 1.10 Invariant Sheaves -- 1.11 The Metatheorem -- 1.12 Stalks of Canonical and Invariant Sheaves -- 1.13 Martindale’s Theorem -- 1.14 Quite Primitive Rings -- 1.15 Rings of Quotients of Quite Primitive Rings -- 2. On Algebraic Independence of Automorphisms And Derivations -- 2.0 Trivial Algebraic Dependences -- 2.1 The Process of Reducing Polynomials -- 2.2 Linear Differential Identities with Automorphisms -- 2.3 Multilinear Differential Identities with Automorphisms -- 2.4 Differential Identities of Prime Rings -- 2.5 Differential Identities of Semiprime Rings -- 2.6 Essential Identities -- 2.7 Some Applications: Galois Extentions of Pi-Rings; Algebraic Automorphisms and Derivations; Associative Envelopes of Lie-Algebras of Derivations -- 3. The Galois Theory of Prime Rings (The Case Of Automorphisms) -- 3.1 Basic Notions -- 3.2 Some Properties of Finite Groups of Outer Automorphisms -- 3.3 Centralizers of Finite-Dimensional Algebras -- 3.4 Trace Forms -- 3.5 Galois Groups -- 3.6 Maschke Groups. Prime Dimensions -- 3.7 Bimodule Properties of Fixed Rings -- 3.8 Ring of Quotients of a Fixed Ring -- 3.9 Galois Subrings for M-Groups -- 3.10 Correspondence Theorems -- 3.11 Extension of Isomorphisms -- 4. The Galois Theory of Prime Rings (The Case Of Derivations) -- 4.1 Duality for Derivations in the Multiplication Algebra -- 4.2Transformation of Differential Forms -- 4.3 Universal Constants -- 4.4 Shirshov Finiteness -- 4.5 The Correspondence Theorem -- 4.6 Extension of Derivations -- 5. The Galois Theory of Semiprime Rings -- 5.1 Essential Trace Forms -- 5.2 Intermediate Subrings -- 5.3 The Correspondence Theorem for Derivations -- 5.4 Basic Notions of the Galois Theory of Semiprime Rings (the case of automorphisms) -- 5.5 Stalks of an Invariant Sheaf for a Regular Group. Homogenous Idempotents -- 5.6 Principal Trace Forms -- 5.7 Galois Groups -- 5.8 Galois Subrings for Regular Closed Groups -- 5.9 Correspondence and Extension Theorems -- 5.10 Shirshov Finiteness. The Structure of Bimodules -- 6. Applications -- 6.1 Free Algebras -- 6.2 Noncommutative Invariants -- 6.3 Relations of a Ring with Fixed Rings -- 6.4 Relations of a Semiprime Ring with Ring of Constants -- 6.5 Hopf Algebras -- References HTTP:URL=https://doi.org/10.1007/978-94-011-3604-4

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