Automorphisms and Derivations of Associative Rings

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.