Largest Maximal Set is a Filter and Largest Minimal Set is an Ideal
Gao Hong-wei · 2001
An equivalent condition that arbitrary element in complete lattice L is a molecular is given.It is shown that largest maximal set α(a)is a filter,when L is a non-trivial complete distributive lattice or the largest element 1 in L isn′t a molecular.Meanwhile,it is proved that largest minimal set β(a) is an ideal,when L is a complete distributive lattice.