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 χ/q is isomorphic to the WUP‐algebra Max(χ), the subalgebra of χ consisting of its maximal elements.
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