On generalized Hilbert algebras

Abstract

In this paper by considering the notion of generalized Hilbert algebra which is named g-Hilbert algebra, we obtain some properties of it.  Moreover, we show that for all n ≥ 3 there exist at least one proper g-Hilbert algebra of order n.  Becaus g-Hilbert algebra is not a Boolean algebra we define the concept of branch in g-Hilbert algebras and we prove that any branch in commutative g-Hilbert algebras is a Boolean algebra.