Quantic格上的同态定理

The homomorphism theorem on Quantic lattices

研究了Quantic格的内部运算,证明了Quantic格中的二元运算&满足结合律的充分必要条件是对任意的a、b、c∈Q,均有a&b→c=a→(b→c).讨论了商Quantic格与核映射之间的关系,证明了Quantic格上的同态定理:设f:P→Q是满的Quantic格同态,则存在P上的核映射j,使得Pj≌Q.

The interior operations of a quantic lattice Q are discussed and it is proved that a sufficient and necessary condition for the binary operation ＆amp; to be associative is a＆amp;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.