Cover Image
Read Now

Automorphisms and Derivations of Associative Rings

Bibliographic Details
Main Author: Kharchenko, V.
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1991, 1991
Edition:1st ed. 1991
Series:Mathematics and its Applications, Soviet Series
Subjects:
Associative Algebras
Commutative Algebra
Commutative Rings And Algebras
Nonassociative Rings
Commutative Rings
Associative Rings
Non-associative Rings And Algebras
Associative Rings And Algebras
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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
  • 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

Similar Items