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Strongness in lattices. (English) Zbl 0826.06003

Summary: U. Faigle [J. Comb. Theory, Ser. B 28, 26-51 (1980; Zbl 0416.05029)] introduced the notion of a strong join-irreducible element in lattices of finite length. In this note we extend the concept of strongness to arbitrary lattices being not necessarily of finite length. Here we give generalizations of some results obtained by Faigle [loc.cit.] and K. Reuter [Acta Math. Hung. 53, No. 1/2, 119-127 (1989; Zbl 0675.06003)].

MSC:

06B05 Structure theory of lattices
06C10 Semimodular lattices, geometric lattices
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