Abstract:
The relationships among Quantic lattices and Quantales,Quantic lattices and distributive lattices are discussed,respectively.It is proved that a left-sided Quantic lattice Q is a commutative Quantale if and only if a→(b→c)=b→(a→c) for all a,b,c∈Q.The concepts of prime elements and S-prime elements in a Quantic lattice are introduced,and some properties of them are discussed.A characterization for an element to be prime is obtained.It is also shown that the image of an S-prime element is an f(S)-prime element when the map f satisfies certain conditions.
