The homomorphism theorem on Quantic lattices
Bin Zhao · Journal of Shaanxi Normal University · 2009
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 ab→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.