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Congruences and ideals in Hilbert algebras. (English) Zbl 0954.08002
A subset \(I\) of a Hilbert algebra \((H;\bullet,1)\) is called an ideal whenever (i) \(1\in I\); (ii) \(a\bullet b\in I\) for \(a\in H\), \(b\in I\); (iii) \((b\bullet (c\bullet a)) \bullet a\in I\) for \(a\in H\), \(b\), \(c\in I\). The authors investigate the relationship between ideals and congruences on Hilbert algebras.
Reviewer: J.Duda (Brno)

MSC:
08A30 Subalgebras, congruence relations
20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)
03G25 Other algebras related to logic
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