Abstract
Congruences and ideals in partial Abelian monoids (PAM) are studied. It is shown that the so-called R 1-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.
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Chevalier, G., Pulmannová, S. Some Ideal Lattices in Partial Abelian Monoids and Effect Algebras. Order 17, 75–92 (2000). https://doi.org/10.1023/A:1006423311104
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DOI: https://doi.org/10.1023/A:1006423311104