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Operational Structures

  • Barbara H. Partee
  • Alice Ter Meulen
  • Robert E. Wall
Part of the Studies in Linguistics and Philosophy book series (SLAP, volume 30)

Abstract

A group G is an algebra which consists of a set G and a single binary operation, which we will usually write as ο, but which may sometimes be written + or x : G = 〈G, ο〉. To be a group, G must satisfy the following conditions, the group axioms:
  1. G1:

    G is an algebra (i.e., ο completely defined and G closed under ο).

     
  2. G2:

    ο is associative.

     
  3. G3:

    G contains an identity element.

     
  4. G4:

    Each element in G has an inverse element.

     

Keywords

Identity Element Integral Domain Positive Element Multiplicative Inverse Positive Rational Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Barbara H. Partee
    • 1
  • Alice Ter Meulen
    • 2
  • Robert E. Wall
    • 3
  1. 1.Department of LinguisticsUniversity of MassachusettsAmherstUSA
  2. 2.Departments of Philosophy and LinguisticsIndiana UniversityBloomingtonUSA
  3. 3.Department of LinguisticsUniversity of TexasAustinUSA

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