ON COVERED PRIME ELEMENTS AND COMPLETE HOMOMORPHISMS OF FRAMES

It is a standard fact that the right adjoints h(*) of general frame homomor- phisms h : L M send prime elements to prime elements. Unlike this, the preservation of covered prime elements by complete frame homomorphism is a special fact. Indeed, if L is totally ordered this happens (for arbitrary M) if and only if L is well-ordered. On the other hand, if M is both a frame and a co-frame there is no restriction on L.This work was motivated by the fact that, in an earlier paper, we erroneously claimed h(*) preserves covered primeness for any complete frame homomorphism h.