On generalized Hilbert algebras - Borzooei, R.A.; Shohani , J. (Italian Journal of Pure and Applied Mathematics, 2012)
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.