Sectionally Pseudocomplemented Residual Lattice

At first, we recall the basic concept, By a residual lattice is meant an algebra ) 1 , 0 , , , , , ( o ∗ ∧ ∨ = L L such that (i) ) 1 , 0 , , , ( ∧ ∨ = L L is a bounded lattice, (ii) ) 1 , , ( ∗ = L L is a commutative monoid, (iii) it satisfies the so-called adjoin ness property: y z y x = ∗ ∨ ) ( if and only if y x z y o ≤ ≤ Let us note [7] that y x ∨ is the greatest element of the set y z y x = ∗ ∨ ) ( Moreover, if we consider y x y x ∧ = ∗ , then y x o is the relative pseudo-complement of x with respect to y, i. e., for ∧ = ∗ 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 } 1 , , , { o ∧ ∨ . We are going to apply a similar approach for the adjointness property: