Mathematicae General Algebra and Applications 21(1) (2001) 21-29
ON DISTRIBUTIVE TRICES
Department of Information Science and Systems
Institute of Mathematics Fac. of Sci., University of
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.
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Received 17 May 1999
Revised 12 March 2001