Whaley's Theorem for Finite Lattices
نویسندگان
چکیده
Whaley’s Theorem on the existence of large proper sublattices of infinite lattices is extended to ordered sets and finite lattices. As a corollary it is shown that every finite lattice L with |L| ≥ 3 contains a proper sublattice S with |S| ≥ |L| 3 . It is also shown that that every finite modular lattice L with |L| ≥ 3 contains a proper sublattice S with |S| ≥ |L| 2 , and every finite distributive lattice L with |L| ≥ 4 contains a proper sublattice S with |S| ≥ 3 4 |L|.
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ورودعنوان ژورنال:
- Order
دوره 20 شماره
صفحات -
تاریخ انتشار 2003