Galois theory for sets of operations closed under permutation, cylindrification, and composition

Miguel Couceiro, Erkko Lehtonen

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

A set of operations on A is shown to be the set of linear term operations of some algebra on A if and only if it is closed under permutation of variables, addition of inessential variables, and composition, and if it contains all projections. A Galois framework is introduced to describe the sets of operations that are closed under the operations mentioned above, not necessarily containing all projections. The dual objects of this Galois connection are systems of pointed multisets, and the Galois closed sets of dual objects are described accordingly. Moreover, the closure systems associated with this Galois connection are shown to be uncountable (even if the closed sets of operations are assumed to contain all projections).

Original languageBritish English
Pages (from-to)273-297
Number of pages25
JournalAlgebra Universalis
Volume67
Issue number3
DOIs
StatePublished - May 2012

Keywords

  • composition
  • cylindrification
  • function algebra
  • Galois connection
  • linear term operation
  • permutation of variables
  • read-once function
  • system of pointed multisets

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