半群中幂等子集的格结构

The lattice structure of idempotent subsets of a semigroup

引进了交半格、交子格与并半格、并子格的概念,讨论了半群S中几类幂等子集的格结构.在此基础上证明了半群的全体幂等子集关于普通集合的包含关系做成完备格,并给出了具体构造上下确界的方法.

First is introduced the notions of interesction semilattice,intersection sublattice,union semilattice and union sublattice,and it discussed the lattice structure to several subsets of power set P(S) of a semigroup S.Based on this it proved that the all idempotent subsets of a semigroup forms a complete lattice with the ordinary subset inclusion  and give a method to structure the sup and inf in the lattice.