Projective pseudo-complemented semilattices

Geoffrey Thomas Jones

Vol. 52 (1974), No. 2, 443–456

DOI: 10.2140/pjm.1974.52.443

Abstract

This paper is concerned with the properties of free, and projective pseudo complemented semilattices (PCSL).

It is proved that a projective PCSL is complemented and all its chains and disjointed subsets are countable, and that a Boolean algebra is projective in the category of PCSL if and only if it is projective in the category of Boolean algebras. Further, necessary and sufficient conditions are established for a finite PCSL to be projective.

Mathematical Subject Classification

Primary: 06A25

Milestones

Received: 20 July 1973

Published: 1 June 1974