Weak pre pseudo effect algebras and generalized weak pre pseudo effect algebras

TL;DR

This paper introduces weak pre pseudo effect algebras and generalized weak pre pseudo effect algebras, extending previous results to a non-commutative setting in the field of algebraic structures related to quantum logic.

Contribution

It generalizes existing algebraic structures to a non-commutative framework, broadening the theoretical foundation of effect algebras.

Findings

Defined weak pre pseudo effect algebras

Established properties of generalized weak pre pseudo effect algebras

Extended results of Chajda and Kühr to non-commutative case

Abstract

Present article concerns the generalization of the results of I. Chajda and J. K\"{u}hr to a non-commutative setting resulting into so called (weak) pre pseudo effect algebras and generalized pre pseudo effect algebras.