  A strongly Fregean algebra is an algebra such that the class of its
homomorphic images is Fregean and the variety generated by this algebra is
congruence modular. To understand the structure of these algebras we study the
prime intervals projectivity relation in the posets of their completely meet
irreducible congruences and show that its cosets have natural structure of
Boolean group. In particular, this approach allows us to represent congruences
and elements of such algebras as the subsets of upward closed subsets of these
posets with some special properties.
