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The Shape of Congruence Lattices
 
Keith A. Kearnes :  University of Colorado, Boulder, CO
Emil W. Kiss :  Loránd Eötvös University, Budapest, Hungary
The Shape of Congruence Lattices
eBook ISBN:  978-0-8218-9515-3
Product Code:  MEMO/222/1046.E
List Price: $83.00
MAA Member Price: $74.70
AMS Member Price: $49.80
Add to cart
The Shape of Congruence Lattices
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The Shape of Congruence Lattices
Keith A. Kearnes :  University of Colorado, Boulder, CO
Emil W. Kiss :  Loránd Eötvös University, Budapest, Hungary
eBook ISBN:  978-0-8218-9515-3
Product Code:  MEMO/222/1046.E
List Price: $83.00
MAA Member Price: $74.70
AMS Member Price: $49.80
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 222; 2013; 169 pp
    MSC: Primary 08

    This monograph is concerned with the relationships between Maltsev conditions, commutator theories and the shapes of congruence lattices in varieties of algebras. The authors develop the theories of the strong commutator, the rectangular commutator, the strong rectangular commutator, as well as a solvability theory for the nonmodular TC commutator. They prove that a residually small variety that satisfies a congruence identity is congruence modular.
  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Preliminary Notions
    • 3. Strong Term Conditions
    • 4. Meet Continuous Congruence Identities
    • 5. Rectangulation
    • 6. A Theory of Solvability
    • 7. Ordinary Congruence Identities
    • 8. Congruence Meet and Join Semidistributivity
    • 9. Residually Small Varieties
    • Problems
    • A. Varieties with Special Terms
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Memoirs of the American Mathematical Society
Volume: 222; 2013; 169 pp
MSC: Primary 08

This monograph is concerned with the relationships between Maltsev conditions, commutator theories and the shapes of congruence lattices in varieties of algebras. The authors develop the theories of the strong commutator, the rectangular commutator, the strong rectangular commutator, as well as a solvability theory for the nonmodular TC commutator. They prove that a residually small variety that satisfies a congruence identity is congruence modular.
  • Chapters
  • 1. Introduction
  • 2. Preliminary Notions
  • 3. Strong Term Conditions
  • 4. Meet Continuous Congruence Identities
  • 5. Rectangulation
  • 6. A Theory of Solvability
  • 7. Ordinary Congruence Identities
  • 8. Congruence Meet and Join Semidistributivity
  • 9. Residually Small Varieties
  • Problems
  • A. Varieties with Special Terms
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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