1. 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