Triple Representation Theorem for homogeneous effect algebras

TL;DR

This paper extends the Triple Representation Theorem to TRT-effect algebras, a specific class of homogeneous effect algebras, broadening its applicability beyond complete lattice effect algebras.

Contribution

It generalizes the Triple Representation Theorem to TRT-effect algebras, including several important subclasses of effect algebras.

Findings

The theorem holds for TRT-effect algebras.

Includes complete lattice effect algebras and other subclasses.

Broadens understanding of effect algebra structures.

Abstract

The aim of our paper is to prove the Triple Representation Theorem, which was established by Jen\v{c}a in the setting of complete lattice effect algebras, for a special class of homogeneous effect algebras, namely TRT-effect algebras. This class includes complete lattice effect algebras, sharply dominating Archimedean atomic lattice effect algebras and homogeneous orthocomplete effect algebras.