A special class of congruences on $${\kappa}$$ κ -frames

Graham Manuell
2017 Algebra Universalis  
Madden has shown that in contrast to the situation with frames, the smallest dense quotient of a κ-frame need not be Boolean. We characterise these so-called d-reduced κ-frames as those which may be embedded as a generating sub-κ-frame of a Boolean frame. We introduce the notion of the closure of a κ-frame congruence and call a congruence clear if it is the largest congruence with a given closure. These ideas are used to prove κ-frame analogues of known results concerning Boolean frame
more » ... . In particular, we show that d-reduced κ-frames are precisely the quotients of κ-frames by clear congruences and that every κ-frame congruence is the meet of clear congruences.
doi:10.1007/s00012-017-0439-y fatcat:4hwfs4pmpfdcdncietc4buy2xy