分子格范畴中一种新的乘积结构

A new product structure in the category of molecular lattices

利用完备格上的关系，在一族分子格｛Ｌｉ｝ｉ∈Ｉ的直积上引入了二元关系，讨论了关系的一些基本性质．借助于关系，在引入了下集的概念，证明了中的所有下集全体按集合包含序构成一个分子格．由此得到了一族分子格在分子格范畴中的乘积结构，并且给出了乘积对象中的全体分子与完全分子．最后证明了一族强分子格在分子格范畴中的乘积对象仍然是强分子格．

The relation on the direct product of a family of molecular lattices {Li}i∈Iis introduced by means of the relation q on complete lattices. Some fundamental properties of the relation are discussed. Based on the relation , the concept of the -lower sets on the direct product is given, and it is proved that the set of all -lower sets on the direct product forms a molecular lattice. Hence, the product structure of a family of molecular lattices in the category of molecular lattices is obtained, and all molecules and completely molecules in the product object are given. It is proved that the product object of a family of strong molecular lattices in the category of molecular lattices is also a strong molecular lattice.