On distributive trices

• Autorzy: Kiyomitsu Horiuchi , Andreja Tepavčević
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

triple semilattice; trice; distributive trice

Kategorie tematyczne

• 08B20: Free algebras
• 08B26: Subdirect products and subdirect irreducibility
• 06A12: Semilattices

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2001
• Tom: 21
• Numer: 1
• Strony: 21-29

Daty

wydano

2001

otrzymano

1999-03-17

poprawiono

2001-03-12

Twórcy

autor

Kiyomitsu Horiuchi

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

autor

Andreja Tepavčević

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

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmgaa.1024