The interior operations of a quantic lattice Q are discussed and it is proved that a sufficient and necessary condition for the binary operation & to be associative is a&b→c=a→(b→c) for all a,b,c∈Q. The relations between quotient quantic lattices and nuclei in a quantic lattice are discussed. At last, a homomorphism theorem is given, which says that if f: P→Q is a surjective homomorphism between quantic lattices, then there is a nucleus j in P such that PjQ.

complete lattice; quantic lattice; homomorphism theorem; nucleus