Every superatomic subalgebra of an interval algebra is embeddable in an ordinal algebra

Uri Abraham, Robert Bonnet

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Let us recall that a Boolean algebra is superatomic if every subalgebra is atomic. So by the definition, every subalgebra of a superatomic algebra is superatomic. An obvious example of a superatomic algebra is the interval algebra generated by a well-ordered chain. In this work, we show that every superatomic subalgebra of an interval algebra is embeddable in an ordinal algebra, that is by definition, an interval algebra generated by a well-ordered chain. As a corollary, if B is aninfinite superatomic subalgebra of an interval algebra, then B and the set At(B) of atoms of B havethe same cardinality.

Original languageEnglish
Pages (from-to)585-592
Number of pages8
JournalProceedings of the American Mathematical Society
Volume115
Issue number3
DOIs
StatePublished - 1 Jan 1992

Keywords

  • Boolean algebras
  • Interval algebras
  • Superatomic boolean algebras

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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