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Representations of Rings over Skew Fields / A.H. Schofield.

A study of representations of rings over skew fields.

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Bibliographic Details
Online Access: Full Text (via Cambridge)
Main Author: Schofield, A. H.
Format: Electronic eBook
Language:English
Published: Cambridge : Cambridge University Press, 1985.
Series:London Mathematical Society lecture note series ; no. 92.
Subjects:
Commutative rings.
Representations of rings (Algebra)
Skew fields.
Table of Contents:
  • Cover
  • Title
  • Copyright
  • Contents
  • Dedication
  • Preface
  • PART I Homomorphisms to simple artinian rings
  • 1 HEREDITARY RINGS AND PROJECTIVE RANK FUNCTIONS
  • Definitions and preliminaries
  • The inner projective rank
  • The torsion modules for a projective rank function
  • 2 THE COPRODUCT THEOREMS
  • The basic coproduct theorems
  • Universal ring constructions
  • 3 PROJECTIVE RANK FUNCTIONS ON RING COPRODUCTS
  • The Generating Number on Ring Coproducts
  • Sylvester projective rank functions on ring coproducts
  • 4. UNIVERSAL LOCALISATION
  • Normal forms for universal localisation.
  • Homological properties of universal localisation
  • Universal localisation and ring coproducts
  • Algebraic K-theory of universal localisation
  • 5 UNIVERSAL HOMOMORPHISMS FROM HEREDITARY TO SIMPLE ARTINIAN RINGS
  • Universal localisation at a Sylvester projective rank function
  • Constructing simple artinian universal localisations
  • Intermediate universal localisations
  • 6. HOMOMORPHISMS FROM HEREDITARY TO VON NEUMANN REGULAR RINGS
  • 7. HOMOMORPHISMS FROM RINGS TO SIMPLE ARTINIAN RINGS
  • Introduction
  • Characterising the homomorphism by the rank function.
  • Universal localisation and Sylvester rank functions
  • Ring coproducts and rank functions
  • Maximal epic subrings and dominions in simple artinian rings
  • The simple artinian spectrum of a k-algebra
  • PART II Skew Subfields of Simple Artinian Coproducts
  • 8 THE CENTRE OF THE SIMPLE ARTINIAN COPRODUCT
  • 9 FINITE DIMENSIONAL DIVISION SUBALGEBRAS OF SKEW FIELD COPRODUCTS
  • Division subalgebras of universal localisations
  • Division subalgebras of simple artinian coproducts
  • General case
  • Division subalgebras of skew field coproducts
  • Transcendence in skew fields.
  • Generic partial splitting skew fields
  • Division subalgebras of the universal skew fields for rings withweak algorithm
  • 10 THE UNIVERSAL BIMODULE OF DERIVATIONS
  • Calculating the universal bimodule of derivations
  • Generators for the free skew field
  • 11 COMMUTATIVE SUBFIELDS AND CENTRALISERS IN SKEW FIELD COPRODUCTS
  • 12 CHARACTERISING UNIVERSAL LOCALISATIONS AT A RANK FUNCTION
  • Simple artinian universal localisations
  • Epic subrings of simple artinian universal localisations of hereditary rings
  • 13 BIMODULE AMALGAM RINGS AND ARTIN'S PROBLEM
  • Bimodule amalgam rings.
  • Isomorphism theorems
  • Artin's problem for skew field extensions
  • An hereditary artinian ring of representation type
  • The construction
  • REFERENCES
  • INDEX.

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