摘要
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) .
出处
《内蒙古大学学报(自然科学版)》
CAS
CSCD
1996年第3期293-296,共4页
Journal of Inner Mongolia University:Natural Science Edition
基金
国家自然科学基金资助项目
关键词
模格μ_(3)
凸子格格
五边形N_(5)
分配格类D
非模格类N_(5)
modular lattice μ_(3)
convex sublattice latice
pentagon N_(5)
equavalence class of distributive lattices D
equavalence class of nonmodular lattices