A triple-semilattice is an algebra with three binary operations, which is a semilattice in respect of each of them. A trice is a triple-semilattice, satisfying so called roundabout absorption laws. In this paper we investigate distributive trices. We prove that the only subdirectly irreducible distributive trices are the trivial one and a two element one. We also discuss finitely generated free distributive trices and prove that a free distributive trice with two generators has 18 elements.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1024,
author = {Kiyomitsu Horiuchi and Andreja Tepav\v cevi\'c},
title = {On distributive trices},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {21},
year = {2001},
pages = {21-29},
zbl = {1001.06006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1024}
}
Kiyomitsu Horiuchi; Andreja Tepavčević. On distributive trices. Discussiones Mathematicae - General Algebra and Applications, Tome 21 (2001) pp. 21-29. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1024/
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