Identities in implicative semilattices

Varieties of Implicative Semilattices

Implicative Identities in Groups

Recently W. McCune and D. A. Sands have considered, in a note Amer Math. Monthly 103 (1996), 888{892], implicative axioms in groups of the form if u = v, then w = t, where u, v, w, t are group words in some variables. Their interest is in such identical implications that deene the variety of groups, or the variety of abelian groups. What I want to present is, slightly more generally, identical ...

Positive Implicative Ordered Filters of Implicative Semigroups

We introduce the notion of positive implicative ordered filters in implicative semigroups. We show that every positive implicative ordered filter is both an ordered filter and an implicative ordered filter. We give examples that an ordered filter (an implicative ordered filter) may not be a positive implicative ordered filter. We also give equivalent conditions of positive implicative ordered f...

Factor Congruences in Semilattices

We characterize factor congruences in semilattices by using generalized notions of order ideal and of direct sum of ideals. When the semilattice has a minimum (maximum) element, these generalized ideals turn into ordinary (dual) ideals. Resumen. En este trabajo damos una caracterización de las congruencias factor en semirret́ıculos usando nociones generalizadas de ideal y suma directa de ideales...

Fuzzy Positive Implicative Ordered Filters of Implicative Semigroups

We consider the fuzzification of the notion of a positive implicative ordered filter in implicative semigroups. We show that every fuzzy positive implicative ordered filter is both a fuzzy ordered filter and a fuzzy implicative ordered filter. We give examples that a fuzzy (implicative) ordered filter may not be a fuzzy positive implicative ordered filter. We also state equivalent conditions of...