On distributive trices
Kiyomitsu Horiuchi; Andreja Tepavčević
Discussiones Mathematicae - General Algebra and Applications (2001)
- Volume: 21, Issue: 1, page 21-29
- ISSN: 1509-9415
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topKiyomitsu Horiuchi, and Andreja Tepavčević. "On distributive trices." Discussiones Mathematicae - General Algebra and Applications 21.1 (2001): 21-29. <http://eudml.org/doc/287634>.
@article{KiyomitsuHoriuchi2001,
abstract = {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.},
author = {Kiyomitsu Horiuchi, Andreja Tepavčević},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {triple semilattice; trice; distributive trice; triple-semilattice; distributive trices},
language = {eng},
number = {1},
pages = {21-29},
title = {On distributive trices},
url = {http://eudml.org/doc/287634},
volume = {21},
year = {2001},
}
TY - JOUR
AU - Kiyomitsu Horiuchi
AU - Andreja Tepavčević
TI - On distributive trices
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2001
VL - 21
IS - 1
SP - 21
EP - 29
AB - 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.
LA - eng
KW - triple semilattice; trice; distributive trice; triple-semilattice; distributive trices
UR - http://eudml.org/doc/287634
ER -
References
top- [1] S. Burris, and H.P. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, New York 1981 (new, electronic version, 1999: is available at the address: www.thoralf.uwaterloo.ca). Zbl0478.08001
- [2] K. Horiuchi, Trice and Two delegates operation, Sci. Math. 2 (1999), 373-384. Zbl0962.06002
- [3] J.A. Kalman, Subdirect decomposition of distributive quasi-lattices, Fund. Math. 71 (1971), 161-163. Zbl0249.06009
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