On a New Construction of Pseudo Effect Algebras

2014/03/07 by Anatolij Dvurečenskij, Dvurečenskij, Anatolij
Computer Science · Decision Sciences · #03G12 #06C15 #81P10 #81P15 #Advanced Algebra and Logic #FOS: Mathematics #FOS: Physical sciences #Fuzzy and Soft Set Theory #Quantum Physics (quant-ph) #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.1403.2289

openalex publication_date 2014/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which is connected not necessarily with partially ordered groups, but rather with generalized pseudo effect algebras where the greatest element is not guaranteed. Starting even with a commutative generalized pseudo effect algebra, we can obtain a non-commutative pseudo effect algebra. We show how such kite pseudo effect algebras are tied with different types of the Riesz Decomposition Properties. We find conditions when kite pseudo effect algebras have the least non-trivial normal ideal.

Citations

• Effect algebras and unsharp quantum logics

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