Ukrainian Mathematical Bulletin

Volume 1, Issue 2, 2004 pp. 279-285.

n-Distributivity and n-Modularity in Lattices

Authors: Joanna Skowronek-Kazi'ow
Author institution: Institute of Mathematics, University of Zielona, Poland

Summary: In this paper, we consider some forbidden sublattices for $n$-distributive, but nonmodular, lattices. We introduce a new notion of $n$-modularity (weaker than $n$-distributivity). We also consider a forbidden sublattice for an $n$-modular lattice. We prove that $n$-modularity implies $(n+1)$-modularity. Counterexamples for the inverse implication are given.

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