Algebra universalis

, Volume 67, Issue 1, pp 81–104 | Cite as

Quotients of dimension effect algebras

  • David J. Foulis
  • Sylvia Pulmannová


We show that the quotient of a dimension effect algebra by its dimension equivalence relation is a unital bounded lattice-ordered positive partial abelian monoid that satisfies a version of the Riesz decomposition property. For a dimension effect algebra of finite type, the quotient is a centrally orthocomplete Stone–Heyting MV-effect algebra; moreover, an orthocomplete effect algebra in which equality is a dimension equivalence relation is the same thing as a complete Stone–Heyting MV-effect algebra.

2010 Mathematics Subject Classification

Primary: 06F99 Secondary: 08A55 03G12 

Keywords and phrases

effect algebra MV-effect algebra Stone–Heyting algebra pseudocomplement orthocomplete centrally orthocomplete dimension effect algebra dimension equivalence relation finite type 


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© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of MassachusettsAmherstUSA
  2. 2.Mathematical InstituteSlovak Academy of SciencesBratislavaSlovakia

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