- Tytuł:
- The exocenter and type decomposition of a generalized pseudoeffect algebra
- Autorzy:
-
Foulis, David
Pulmannová, Silvia
Vinceková, Elena - Powiązania:
- https://bibliotekanauki.pl/articles/728938.pdf
- Data publikacji:
- 2013
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
pseudoeffect algebra
generalized pseudoeffect algebra
center
exocenter
central orthocompleteness
type determining set
type decomposition - Opis:
- We extend the notion of the exocenter of a generalized effect algebra (GEA) to a generalized pseudoeffect algebra (GPEA) and show that elements of the exocenter are in one-to-one correspondence with direct decompositions of the GPEA; thus the exocenter is a generalization of the center of a pseudoeffect algebra (PEA). The exocenter forms a boolean algebra and the central elements of the GPEA correspond to elements of a sublattice of the exocenter which forms a generalized boolean algebra. We extend the notion of central orthocompleteness to GPEA, prove that the exocenter of a centrally orthocomplete GPEA (COGPEA) is a complete boolean algebra and show that the sublattice corresponding to the center is a complete boolean subalgebra. We also show that in a COGPEA, every element admits an exocentral cover and that the family of all exocentral covers, the so-called exocentral cover system, has the properties of a hull system on a generalized effect algebra. We extend the notion of type determining (TD) sets, originally introduced for effect algebras and then extended to GEAs and PEAs, to GPEAs, and prove a type-decomposition theorem, analogous to the type decomposition of von Neumann algebras.
- Źródło:
-
Discussiones Mathematicae - General Algebra and Applications; 2013, 33, 1; 13-47
1509-9415 - Pojawia się w:
- Discussiones Mathematicae - General Algebra and Applications
- Dostawca treści:
- Biblioteka Nauki
Artykuł