On Blo-algebras
Joemar C. Endam, Alice A. Mamhot · Asian-European Journal of Mathematics · 2022
A B-algebra is an algebra [Formula: see text] of type (2, 0) satisfying: (I) [Formula: see text], (II) [Formula: see text], (III) [Formula: see text]. A B[Formula: see text]-algebra is an algebra [Formula: see text] such that [Formula: see text] is a B-algebra and [Formula: see text] is a poset with [Formula: see text] compatible on [Formula: see text]. In this paper, we introduce and characterize lattice ordered B-algebras (or B[Formula: see text]-algebras). A B[Formula: see text]-algebra is a B[Formula: see text]-algebra which is a lattice under its partial order. We show that a B[Formula: see text]-algebra is both distributive and torsion-free.