Chajda, I.; Halaš, R. Congruences and ideals in Hilbert algebras. (English) Zbl 0954.08002 Kyungpook Math. J. 39, No. 2, 429-432 (1999). 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) Cited in 2 ReviewsCited in 9 Documents 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 PDFBibTeX XMLCite \textit{I. Chajda} and \textit{R. Halaš}, Kyungpook Math. J. 39, No. 2, 429--432 (1999; Zbl 0954.08002)