Orrin Frink in 1962 stated incorrectly, that there exist free pseudocomplemented meet-semilattices, which are not lattices. This is disproved in the present paper. We have shown that any free PCS is in fact a sectionally pseudocomplemented lattice.

An intrinsic characterization of free pseudocomplemented semilattices is presented. The second principal result gives a method for constructing free pseudocomplemented semilattices.

Recently, Grätzer, Gunderson and Quackenbush have characterized the spectra of finite pseudocomplemented lattices, solving a problem raised by G. Grätzer in his first monograph on lattice theory from 1971. In this note we discuss the tight connection between the spectra and the Glivenko congruence of finite pseudocomplemented lattices.

Sabine Koppelberg has introduced and studied the notion of projective extensions of Boolean algebras. Our aim is to characterize the projective extensions of semilattices.

S. Burris and H. Werner [1] introduced a (weak) Boolean product of algebras. It is a special subdirect product over a Boolean space. It was shown in [1] that the (weak) Boolean product of algebras is equivalent to the formation of global sections of sheaves of algebras over Boolean spaces. In this paper we show that every non-trivial double Stone algebra can be characterized in terms of weak Boolean products of pure double Stone algebras. Using this technique, a new characterization of the free (regular) double Stone algebras is given.

It is well known (Lee [13]) that the class of all distributive p-algebras B = Bω is a variety and that the class of all subvarieties of B forms a chainwhere B-i is the trivial class, B0 is the class of Boolean algebras, and B1 is the class of Stone algebras.