SECTIONALLY PSEUDOCOMPLEMENTED RESIDUAL LATTICE

Abstract

At first, we recall the basic concept, By a residual lattice is meant an algebra L = (L,¡ý,¡ü,.,o,0,1) such that (i) L = (L,¡ý,¡ü,0,1) is a bounded lattice, (ii) L = (L,.,1) is a commutative monoid, (iii) it satisfies the so-called adjoin ness property: (x ¡ý y) . z = y if and only if y ¡Â z ¡Â x o y Let us note [7] that x ¡ý y is the greatest element of the set (x ¡ý y) . z = y Moreover, if we consider x . y = x ¡ü y , then x o y is the relative pseudo-complement of x with respect to y, i. e., for . = ¡ü residuated lattices are just relatively pseudo-complemented lattices. The identities characterizing sectionally pseudocomplemented lattices are presented in [3] i.e. the class of these lattices is a variety in the signature {¡ý,¡ü,o,1}. We are going to apply a similar approach for the adjointness property: