Strong, Balanced, and Consistent Lattices
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FAIGLE [1980 b] introduced the notion of a strong join-irreducible in lattices of finite length (s. Definition 16.2 below). Using the concepts a′ and a+ (s. Section 10) we present two extensions of Faigle’s concept of a strong join-irreducible, namely the notion of a strong element and the notion of a strict element. Both notions will turn out to be useful for our subsequent considerations.
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