Atomicity of lattice effect algebras and their sub-lattice effect algebras

Title:

Atomicity of lattice effect algebras and their sub-lattice effect algebras

Creator:

Paseka, Jan and Riečanová, Zdenka

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:ce9f1c28-a2bb-45c3-ad9a-e0b2ce3fd5cb
uuid:ce9f1c28-a2bb-45c3-ad9a-e0b2ce3fd5cb

Subject:

non-classical logics, D-posets, effect algebras, MV-algebras, and atomicity

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We show some families of lattice effect algebras (a common generalization of orthomodular lattices and MV-effect algebras) each element E of which has atomic center C(E) or the subset S(E) of all sharp elements, resp. the center of compatibility B(E) or every block M of E. The atomicity of E or its sub-lattice effect algebras C(E), S(E), B(E) and blocks M of E is very useful equipment for the investigations of its algebraic and topological properties, the existence or smearing of states on E, questions about isomorphisms and so. Namely we touch the families of complete lattice effect algebras, or lattice effect algebras with finitely many blocks, or complete atomic lattice effect algebra E with Hausdorff interval topology.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[1040]-1051

Source:

Kybernetika | 2009 Volume:45 | Number:6

Harvested from:

CDK

Metadata only:

false