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Discussiones Mathematicae General Algebra and Applications 21(1) (2001) 21-29
DOI: https://doi.org/10.7151/dmgaa.1024

ON DISTRIBUTIVE TRICES

Kiyomitsu Horiuchi Department of Information Science and Systems Engineering, Faculty of Science and Engineering, Konan University Okamoto, Higashinada, Kobe 658-8501, Japan e-mail: horiuchi@konan-u.ac.jp

Andreja Tepavcević Institute of Mathematics Fac. of Sci., University of Novi Sad Trg D. Obradovića 4, 21000 Novi Sad Yugoslavia e-mail:etepavce@EUnet.yu

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.

Keywords and phrases: triple semilattice, trice, distributive trice.

2000 Mathematics Subject Classification: 06A12, 08B20, 08B26.

References

[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).
[2]	K. Horiuchi, Trice and Two delegates operation, Sci. Math. 2 (1999), 373-384.
[3]	J.A. Kalman, Subdirect decomposition of distributive quasi-lattices, Fund. Math. 71 (1971), 161-163.

Received 17 May 1999
Revised 12 March 2001