title: The structure of separable Dynkin algebras
metadata.name: dc.contributor.author
metadata.value: Vallander, Sergey S.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-09-28T15:34:08Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-09-28T15:34:08Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vallander S. S. The structure of separable Dynkin algebras. Vestnik of Saint Petersburg University. Series 1. Mathematics. Mechanics. Astronomy, 2016, vol. 3 (61), issue 3, pp. 377– 383.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2016.304
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/3906
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We continue to study abstract Dynkin algebras introduced in [2]. Such algebras form a useful instrument
  for discussing probabilities in a rather natural context. Abstractness means the absence of a set-theoretic
  structure of elements in such algebras. We introduce a large useful class of abstract algebras — separable
  Dynkin algebras and indicate also the simplest example of a non-separable algebra. The property of
  separability allows us to define appropriate variants of Boolean versions to operations of intersection and
  union of elements. Such operations are in general only partially defined. Some properties of separable
  algebras are proved. We use them to receive the standard properties of intersection and union including
  associativity and distributivity in case the corresponding operations are applicable. The established facts
  allow us to define Boolean subalgebras in a separable Dynkin algebra and to check the coincidence of our
  version of definition with a usual one.
  Finally we formulate and prove the main result about structure of separable Dynkin algebras — we
  represent them as a set-theoretic union of maximal Boolean subalgebras. The proof uses earlier done
  preparation and standard scheme of Zorn lemma application. Refs 6.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Series 1. Mathematics. Mechanics. Astronomy;Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: abstract Dynkin algebras
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Boolean operations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: separable Dynkin algebras
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: The structure of separable Dynkin algebras
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: Vallander.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/3906/1/Vallander.pdf
resources.format: Adobe PDF
resources.size: 188,38 kB