Quasi-Subalgebras and quasi-congruences for Quasi-Modal lattices
by
Jorge Ernesto Castro
Universidad de Barcelona
Coauthors: Sergio Arturo Celani

The principal ideas of this work are based on the paper Quasi-Modal Algebras, by Celani S (Quasi-Modal Algebras.  Mathematica Bohemica Vol. 126, No. 4 (2001), 721-736), and the preprint Remarks on Quasi-Modal Algebras, by the same author. A quasi-modal algebra is a structure A= á A, /\ , \/ , \lnot, \Delta, 0, 1 ñ , where á A, /\ , \/ , \lnot, 0, 1 ñ is a boolean algebra, \Delta is a function \Delta:A --> Id(A), and Id( A) denotes the set of all ideals of A, such that verifies

1.  \Delta( a /\ b) = \Delta( a) \cap \Delta( b)

2.  \Delta1 = A

A function Ñ:A --> Fi( A) , is also defined in terms of the negation \lnot, where Fi( A) denotes the set of all filters of A. Adequate definitions are introduced in the previous references,  from which the concept of homomorphism between two quasi-modal algebras follows, also the notion of congruence in these new structures, etc..  In our work, such studies are extended to bounded distributive lattices, obtaining somehow more general results.

Date received: February 27, 2003