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On midpoints in lattices. (English) Zbl 0821.06005

Summary: This paper introduces the notion of a midpoint in a lattice \(L\) having a zero element and the notion of a centred ideal in \(L\). It is shown that the study of centred ideals in sectionally complemented lattices is facilitated by a congruence \(\theta (I)\). The congruence \(\theta (I)\) is compared with some other known congruences. A complete characterization of centred ideals in such lattices is given.

MSC:

06B10 Lattice ideals, congruence relations
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