完备剩余幂集格的经典同构对象

摘要

本文在格L是完备剩余格的条件下,引入关于L-1集合套的张量积和蕴涵运算,证明了L-2集合套关于这2种运算构成完备剩余格.本文还进一步证明该完备剩余格恰好与完备剩余幂集格是同构的,从而建立起完备剩余格环境下的L-集表现定理.%In this paper, the tensor and residuum operations of L-nested systems are introduced under the condition that the lattice is a complete residuated lattice. Then we show L-nested systems form a complete residuated lattice, which is precisely the classical isomorphic object of complete residuated power set lattice. Thus the new representation theorem of L-subsets on the condition of complete residuated lattice is obtained in the paper.