Some ideal lattices in partial Abelian monoids and effect algebras

被引：30

作者：

Chevalier, G

Pulmannová, S

机构：

[1] Univ Lyon 1, Inst Girard Desargues, UPRES A 5028, F-69622 Villeurbanne, France

[2] Slovak Acad Sci, Dept Math, Bratislava 81473, Slovakia

来源：

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 2000年 / 17卷 / 01期

关键词：

congruence; dimension equivalence; effect algebra; ideal; lattice of ideals; partial Abelian monoid; R-1-ideal; Riesz ideal; Sasaki projection;

D O I：

10.1023/A:1006423311104

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：75 / 92

页数：18

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