Search

Start Over Subject pseudo-effect algebra

1. Compatibility and central elements in pseudo-effect algebras

Creator:
Vitolo, Paolo
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
pseudo-effect algebra, lattice-pseudo--effect algebra, pseudo-MV-algebra, compatible elements, and central element
Language:
English
Description:
An equivalent definition of compatibility in pseudo-effect algebras is given, and its relationships with central elements are investigated. Furthermore, pseudo-MV-algebras are characterized among pseudo-effect algebras by means of compatibility.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Holland’s theorem for pseudo-effect algebras

Creator:
Dvurečenskij, Anatolij
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
pseudo-effect algebra, pseudo $MV$-algebra, antilattice, prime ideal, automorphism, unital po-group, and unital $\ell $-group
Language:
English
Description:
We give two variations of the Holland representation theorem for $\ell $-groups and of its generalization of Glass for directed interpolation po-groups as groups of automorphisms of a linearly ordered set or of an antilattice, respectively. We show that every pseudo-effect algebra with some kind of the Riesz decomposition property as well as any pseudo $MV$-algebra can be represented as a pseudo-effect algebra or as a pseudo $MV$-algebra of automorphisms of some antilattice or of some linearly ordered set.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public