Some Results about Weak UP-algebras

Abstract

We introduce a new class of algebras, weak UP-algebras, briefly written as WUP-algebras, as a wider class than the classes of UP-algebras and KU-algebras. We investigate fundamental aspects including maximal elements, branches and the subalgebra consisting of maximal elements of a WUP-algebra. We also study regular congruences on a WUP-algebra as well as the corresponding quotient WUP-algebras. We prove that the congruence generated from the branches of a WUP-algebra is regular and the corresponding quotient algebra $\chi /q$ is isomorphic to the WUP-algebra $\text{Max}\left(\chi \right)$ , the subalgebra of $\chi$ consisting of its maximal elements.