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

Lehtonen, Erkko; Couceiro, Miguel (2012), Galois theory for sets of operations closed under permutation, cylindrification and composition, Algebra Universalis, 67, 3, p. 273-297. http://dx.doi.org/10.1007/s00012-012-0184-1

Type
Article accepté pour publication ou publié
Date
2012
Journal name
Algebra Universalis
Volume
67
Number
3
Publisher
Springer
Pages
273-297
Publication identifier
http://dx.doi.org/10.1007/s00012-012-0184-1
Metadata
Show full item record
Author(s)
Lehtonen, Erkko cc
Couceiro, Miguel
Abstract (EN)
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).
Subjects / Keywords
Linear term operation; read-once function; function algebra; Galois connection; system of pointed multisets; permutation of variables; cylindrification; composition

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