The submaximal clones on the three-element set with finitely many relative R-classes

Erkko Lehtonen; Ágnes Szendrei

Discussiones Mathematicae - General Algebra and Applications (2010)

  • Volume: 30, Issue: 1, page 7-33
  • ISSN: 1509-9415

Abstract

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For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A if and only if each one is a substitution instance of the other using operations from C. We study the maximal and submaximal clones on a three-element set and determine which of them have only finitely many relative R-classes.

How to cite

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Erkko Lehtonen, and Ágnes Szendrei. "The submaximal clones on the three-element set with finitely many relative R-classes." Discussiones Mathematicae - General Algebra and Applications 30.1 (2010): 7-33. <http://eudml.org/doc/276698>.

@article{ErkkoLehtonen2010,
abstract = {For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A if and only if each one is a substitution instance of the other using operations from C. We study the maximal and submaximal clones on a three-element set and determine which of them have only finitely many relative R-classes.},
author = {Erkko Lehtonen, Ágnes Szendrei},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {clone; maximal clone; submaximal clone; Green 's relations; Green's relations},
language = {eng},
number = {1},
pages = {7-33},
title = {The submaximal clones on the three-element set with finitely many relative R-classes},
url = {http://eudml.org/doc/276698},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Erkko Lehtonen
AU - Ágnes Szendrei
TI - The submaximal clones on the three-element set with finitely many relative R-classes
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2010
VL - 30
IS - 1
SP - 7
EP - 33
AB - For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A if and only if each one is a substitution instance of the other using operations from C. We study the maximal and submaximal clones on a three-element set and determine which of them have only finitely many relative R-classes.
LA - eng
KW - clone; maximal clone; submaximal clone; Green 's relations; Green's relations
UR - http://eudml.org/doc/276698
ER -

References

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