凸子格格Csub(L)含有μ_(3)的充要条件

Necessary and Sufficient Condition for a Convex Sublattice Lattice Csub(L) to have a Sublattice isomorphic to μ_(3)

给出了有限格Ｌ的凸子格格Ｃｓｕｂ（Ｌ）含有３的一个充要条件，同时就Ｌ的无限情形也进行了讨论并得到了相应结果，把这些结果推广到了ｋ（ｋ≥３）的情形．从而得出了Ｃｓｕｂ（ ） ｎ∨Ｎ５．

A necessary and sufficient condition for a convex sublattice lattice Csub(L) to have a sublattice isomorphic to M3(and Mn) is obtained. The following theorem is proved.Theorem Let (L, ∨,∧). be a finite lattice. Then Csub(L) has a Sublattice isomorphic toM.n if and only if there Are (a1,a'1), (a2,a'2),... (an,a'n) ∈L ×L,such that1) (ai,a'i)≠ (aj,a'j) (i≠j) ； 2) ai≤a'i. (i= 1,2 1 ...，n)；3) 4) .