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, Volume 17, Issue 1, pp 75–92 | Cite as

Some Ideal Lattices in Partial Abelian Monoids and Effect Algebras

  • G. Chevalier
  • S. Pulmannová
Article

Abstract

Congruences and ideals in partial Abelian monoids (PAM) are studied. It is shown that the so-called R1-ideals in cancellative PAMs (CPAM) form a complete Brouwerian sublattice of the lattice of all ideals, and they are standard elements of it. In a special class of CPAMs, effect algebras, properties of ideals and congruences are studied in relation to the generalized Sasaki projections and dimensional equivalence.

congruence dimension equivalence effect algebra ideal lattice of ideals partial Abelian monoid R1-ideal Riesz ideal Sasaki projection 

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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • G. Chevalier
    • 1
  • S. Pulmannová
    • 2
  1. 1.Institut Girard Desargues (UPRES A 5028)Université Lyon 1Villeurbanne CedexFrance
  2. 2.Mathematical DepartmentSlovak Academy of SciencesBratislavaSlovakia

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