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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
##### Keywords:
Hilbert algebra; ideal; congruences