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Inhaltsverzeichnis
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.
