On congruence distributivity of ordered algebras with constants

Krisztina Balog; Benedek Skublics

Discussiones Mathematicae - General Algebra and Applications (2011)

  • Volume: 31, Issue: 1, page 47-59
  • ISSN: 1509-9415

Abstract

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We define the order-congruence distributivity at 0 and order- congruence n-distributivity at 0 of ordered algebras with a nullary operation 0. These notions are generalizations of congruence distributivity and congruence n-distributivity. We prove that a class of ordered algebras with a nullary operation 0 closed under taking subalgebras and direct products is order-congruence distributive at 0 iff it is order-congruence n-distributive at 0. We also characterize such classes by a Mal'tsev condition.

How to cite

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Krisztina Balog, and Benedek Skublics. "On congruence distributivity of ordered algebras with constants." Discussiones Mathematicae - General Algebra and Applications 31.1 (2011): 47-59. <http://eudml.org/doc/276515>.

@article{KrisztinaBalog2011,
abstract = {We define the order-congruence distributivity at 0 and order- congruence n-distributivity at 0 of ordered algebras with a nullary operation 0. These notions are generalizations of congruence distributivity and congruence n-distributivity. We prove that a class of ordered algebras with a nullary operation 0 closed under taking subalgebras and direct products is order-congruence distributive at 0 iff it is order-congruence n-distributive at 0. We also characterize such classes by a Mal'tsev condition.},
author = {Krisztina Balog, Benedek Skublics},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {ordered algebra; n-distributivity; distributivity; Mal'tsev condition; -distributivity},
language = {eng},
number = {1},
pages = {47-59},
title = {On congruence distributivity of ordered algebras with constants},
url = {http://eudml.org/doc/276515},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Krisztina Balog
AU - Benedek Skublics
TI - On congruence distributivity of ordered algebras with constants
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2011
VL - 31
IS - 1
SP - 47
EP - 59
AB - We define the order-congruence distributivity at 0 and order- congruence n-distributivity at 0 of ordered algebras with a nullary operation 0. These notions are generalizations of congruence distributivity and congruence n-distributivity. We prove that a class of ordered algebras with a nullary operation 0 closed under taking subalgebras and direct products is order-congruence distributive at 0 iff it is order-congruence n-distributive at 0. We also characterize such classes by a Mal'tsev condition.
LA - eng
KW - ordered algebra; n-distributivity; distributivity; Mal'tsev condition; -distributivity
UR - http://eudml.org/doc/276515
ER -

References

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