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Weak relative pseudocomplements in semilattices

Cirulis J.

Demonstratio Mathematica

2011

Vol. 44, nr 4

651-672

Weak relative pseudocomplementation on a meet semilattice S is a partial operation * which associates with every pair (x, y) of elements, where (…) an element z (the weak pseudocomplement of x relative to y which is the greatest among elements u such that (…). The element z coincides with the pseudocomplement of x in the upper section [y) and, if S is modular, with the pseudocomplement of x relative to y A weakly relatively pseudomented semilattice is said to be extended, if it is equipped with a total binary operation extending *. We study congruence properties of the variety of such semilattices and review some of its subvarieties already described in the literature.