ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

Discussiones Mathematicae - General Algebra and Applications

Cite Score: 0.4

SJR: 0.203

SNIP: 0.562

MCQ: 0.12

Index Copernicus: 120.64

Discussiones Mathematicae - General Algebra and Applications


Discussiones Mathematicae General Algebra and Applications 21(1) (2001) 21-29


Kiyomitsu Horiuchi

Department of Information Science and Systems Engineering,
Faculty of Science and Engineering, Konan University
Okamoto, Higashinada, Kobe 658-8501, Japan


Andreja Tepavcević

Institute of Mathematics Fac. of Sci., University of Novi Sad
Trg D. Obradovića 4, 21000 Novi Sad Yugoslavia



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.


[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:
[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