完备格的商格的分配性

The Distributivity of Quotient Lattices

本文利用对任意交封闭的完备格上的同余关系得到了一个与商格同构的完备格的序子格。利用该序子格为交闭子格的附加条件,得到了商格满足原完备格所具有的分配性的统一条件。另外,还证明了完全分配格的完备同态象必同构于它自身的一个序子格。

In this paper, define in a complete lattice a meet-closed congruence relation, which brings about for the complete lattice an order sublattice isomorphic to the quotient lattice of the meet-closed congruence relation. with this order Sublattice of the complete lattice, we obtain a uniform sufficient condition for the quotient lattice to maintain the distributivity of the complete lattice. Moreover, we proof that any complete homomorphie image of a complete lattice is isomorphic to one of its own order sublattices.