摘要
证明了如下结果 :设L是完备格 ,L是完备集环 L同构到L的完全并既约元有限生成的分配并半格F上的理想格I(F) .完备格L同构到一个格K的理想格I(K) ,L是完备集环
In this paper,The results below are proved:A complete lattice L is a complete ring of sets (LI(F),I(F)) is the lattice of all ideals of F,and F is a distributive join semilattice which is finitely generated by the set of all completely join irreducible elements of L.If a complete lattice L is isomorphic to the ideal lattice of a lattice K,i.e.,I(K)L,then L is a complete ring of sets K is a strong Sober lattice.
出处
《内蒙古师范大学学报（自然科学汉文版）》
CAS
2004年第2期124-127,共4页
Journal of Inner Mongolia Normal University(Natural Science Edition)
关键词
完备集环
理想格
完全并既约元
分配并半格
强Sober格
刻划
满射
complete rings of sets
completely join-irreducible elements
ideal lattices
join-irreducible (elements)
strong Sober lattices
