Advertisement

Basic Concepts of Algebra

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

Abstract

An algebra A is a set A together with one or more operations f i . We may represent an algebra by writing
$${\rm{ }}A = \left\langle {A,{\rm{ }}{f_1},{\rm{ }}{f_2}{\rm{ }}...{\rm{, }}{f_n}} \right\rangle$$
(9-1)
or by using particular symbols for the operations, such as
$${\rm{ }}{\bf{A}}{\rm{ = }}\left\langle {A,{\rm{ + , }} \times } \right\rangle$$
(9-2)
The set A may be finite or infinite, and there may be either a finite or an infinite number of different operations. However, each operation must be finitary, i.e. unary, binary, ternary .... Each n-ary operation must be a well-defined operation, i.e., defined for all n-tuples of elements of A and yielding a unique element of A as a value for each n-tuple (cf. the mapping condition for functions in Section 2.3).

Keywords

Identity Element Left Identity Zero Element Logical Conjunction Function Composition 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations