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ArticleOriginal scientific text

Title

On distributive trices

Authors 1, 2

Affiliations

  1. Department of Information Science and Systems Engineering, Faculty of Science and Engineering, Konan University, Okamoto, Higashinada, Kobe 658-8501, Japan
  2. Institute of Mathematics Fac. of Sci., University of Novi Sad, Trg D. Obradovića 4, 21000 Novi Sad Yugoslavia

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

ENG
triple semilattice, trice, distributive trice

Bibliography

  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.
Discussiones Mathematicae - General Algebra and Applications
2001/21/1
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Pages:
21-29
Main language of publication
English
Received
1999-03-17
Accepted
2001-03-12
Published
2001

DOI: 10.7151/dmgaa.1024

Exact and natural sciences