International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 82318, 4 pages
On a characterization of the lattice of subsystems of a transition system
Department of Mathematics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Yaoundé, Cameroon
Received 4 October 2005; Revised 20 May 2006; Accepted 28 May 2006
Copyright © 2006 J. P. Mavoungou and C. Nkuimi-Jugnia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
It was first proved by Birkhoff and Frink, and the result now
belongs to the folklore, that any algebraic lattice is up to
isomorphism the lattice of subuniverses of a universal
algebra. A study of subsystems of a transition system
yields a new algebraic concept, that of a strongly algebraic
lattice. We give here a representation theorem to the manner of
Birkhoff and Frink of such lattices.