Geodesic
Compatible Idempotent Terms in Universal Algebra
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 53 (2014) no. 2, pp. 35-51.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In universal algebra, we oftentimes encounter varieties that are not especially well-behaved from any point of view, but are such that all their members have a “well-behaved core”, i.e. subalgebras or quotients with satisfactory properties. Of special interest is the case in which this “core” is a retract determined by an idempotent endomorphism that is uniformly term definable (through a unary term $t(x)$) in every member of the given variety. Here, we try to give a unified account of this phenomenon. In particular, we investigate what happens when various congruence properties—like congruence distributivity, congruence permutability or congruence modularity—are not supposed to hold unrestrictedly in any $\mathbf {A}\in \mathcal {V}$, but only for congruence classes of values of the term operation $t^{\mathbf {A}}$.
Classification : 03C05, 08A30, 08B10
Keywords: Congruence distributive variety; congruence modular variety; congruence permutable variety; idempotent endomorphism 
@article{AUPO_2014__53_2_a2,
     author = {Chajda, Ivan and Ledda, Antonio and Paoli, Francesco},
     title = {Compatible {Idempotent} {Terms} in {Universal} {Algebra}},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
     pages = {35--51},
     publisher = {mathdoc},
     volume = {53},
     number = {2},
     year = {2014},
     mrnumber = {3331005},
     zbl = {1315.08001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPO_2014__53_2_a2/}
}
TY  - JOUR
AU  - Chajda, Ivan
AU  - Ledda, Antonio
AU  - Paoli, Francesco
TI  - Compatible Idempotent Terms in Universal Algebra
JO  - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY  - 2014
SP  - 35
EP  - 51
VL  - 53
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUPO_2014__53_2_a2/
LA  - en
ID  - AUPO_2014__53_2_a2
ER  - 
%0 Journal Article
%A Chajda, Ivan
%A Ledda, Antonio
%A Paoli, Francesco
%T Compatible Idempotent Terms in Universal Algebra
%J Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
%D 2014
%P 35-51
%V 53
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUPO_2014__53_2_a2/
%G en
%F AUPO_2014__53_2_a2
Chajda, Ivan; Ledda, Antonio; Paoli, Francesco. Compatible Idempotent Terms in Universal Algebra. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 53 (2014) no. 2, pp. 35-51. http://geodesic.mathdoc.fr/item/AUPO_2014__53_2_a2/