2019/12/30 by Haviar, Miroslav, Ploščica, Miroslav
#06B10 #06D30 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1912.12891
An algebra \mathbb A is called a perfect extension of its subalgebra \mathbb B if every congruence of \mathbb B has a unique extension to \mathbb A. This terminology was used by Blyth and Varlet [1994]. In the case of lattices, this concept was described by Grätzer and Wehrung [1999] by saying that \mathbb A is a congruence-preserving extension of \mathbb B. Not many investigations of this concept have been carried out so far. The present authors in another recent study faced the question of when a de Morgan algebra \mathbb M is perfect extension of its Boolean subalgebra B(\mathbb M), the so-called skeleton of \mathbb M. In this note a full solution to this interesting problem is given. The theory of natural dualities in the sense of Davey and Werner [1983] and Clark and Davey [1998], as well as Boolean product representations, are used as the main tools to obtain the solution.