Some Ideal Lattices in Partial Abelian Monoids and Effect Algebras |
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| Authors: | Chevalier G Pulmannová S |
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| Institution: | (1) Institut Girard Desargues (UPRES A 5028), Université Lyon 1, bat 101, 43, Boulevard du 11 Novembre 1918, F 69622 Villeurbanne Cedex, France;(2) Mathematical Department, Slovak Academy of Sciences,  tefánikova 49, 814 73 Bratislava, Slovakia |
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| 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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| Keywords: | congruence dimension equivalence effect algebra ideal lattice of ideals partial Abelian monoid R
1-ideal Riesz ideal Sasaki projection |
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