Every Skew Effect Algebra can be Extended into a Total Algebra
Ivan Chajda and Miroslav Kolarik
Skew effect algebras were already introduced as a non-associative modification of the so-called effect algebras which serve as an algebraic axiomatization of the propositional logic of quantum mechanics. Since skew effect algebras have a partial binary operation, we search for an algebra with a total binary operation which extends a given skew effect algebra and such that the underlying posets coincide. It turns out that the suitable candidate is a skew basic algebra introduced here. Algebraic properties of skew basic algebras are described and they are compared with the so-called pseudo basic algebras introduced by the authors recently.
Keywords: Skew basic algebra, pseudo basic algebra, commutative directoid, skew effect algebra, sectional switching involutions.
MS Classification: 03G25, 06A06, 06F99, 08A55