格蕴涵代数的superior滤子

The Superior Filters of the Lattice Implication Algebras

从一个新的角度对格蕴涵代数的滤子理论作进一步研究。给定一个具有最小元的偏序集,提出了格蕴涵代数superior滤子和superior关联滤子的概念,研究了superior滤子的相关性质,给出了若干等价刻画。讨论了superior滤子和superior关联滤子相关关系。最后还得到了上确界关联滤子的一些等价刻画。

In this paper, from new point of view, the filter theory in lattice implication algebras is studied further. Given a poset with the smallest element, the concept of superior filters and superior implicative filters are introduced in the lattice implications algebras; Some properties of superior filters are also discussed, and various equivalent characterization of superior filters are given. Besides, the relationship between superior filters and superior implicative filters are also discussed; Finally, we get some equivalent characterization of superior Implicative filters.