Distributivep-algebras and doublep-algebras havingn-permutable congruences
R. Beazer · Proceedings of the Edinburgh Mathematical Society · 1992
Recent research on aspects of distributive lattices,p-algebras, doublep-algebras and de-Morgan algebras (see [2] and the references therein) has led to the consideration of the classes (n≧1) of distributive lattices having non+ 1-element chain in their poset of prime ideals. In [1] we were obliged to characterize the members of by a sentence in the first-order theory of distributive lattices. Subsequently (see [2]), it was realised that coincides with the class of distributive lattices havingn+1-permutable congruences. This result is hereby employed to describe those distributivep-algebras and doublep-algebras havingn-permutable congruences. As an application, new characterizations of those distributivep-algebras and doublep-algebras having the property that their compact congruences are principal are obtained. In addition, those varieties of distributivep-algebras and doublep-algebras havingn-permutable congruences are announced.