  We prove that assuming suitable cardinal arithmetic, if B is a Boolean
algebra every homomorphic image of which is isomorphic to a factor, then B has
locally small density. We also prove that for an (infinite) Boolean algebra B,
the number of subalgebras is not smaller than the number of endomorphisms, and
other related inequalities. Lastly we deal with the obtainment of the supremum
of the cardinalities of sets of pairwise incomparable elements of a Boolean
algebra.
