1. Lattice effect algebras densely embeddable into complete ones
- Creator:
- Riečanová, Zdenka
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- non-classical logics, orthomodular lattices, effect algebras, MV-algebras, and Mac-Neille completions
- Language:
- English
- Description:
- An effect algebraic partial binary operation ⊕ defined on the underlying set E uniquely introduces partial order, but not conversely. We show that if on a MacNeille completion Eˆ of E there exists an effect algebraic partial binary operation ⊕ˆ then ⊕ˆ need not be an extension of ⊕. Moreover, for an Archimedean atomic lattice effect algebra E we give a necessary and sufficient condition for that ⊕ˆ existing on Eˆ is an extension of ⊕ defined on E. Further we show that such ⊕ˆ extending ⊕ exists at most one.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public