效应代数上态射的一些性质

摘要

Some properties of morphisms of effect algebras,morphism,monomorphisms and weak mono-morphisms are discussed. It is proved that if E1 ,E2 are lattice effect algebras and φ;E1+E2 is an injectivemorphism and a lattice homomorphism, then φ is a monomorphism; conversely, a surjective monomor-phism φ: E1 →E2 must be a lattice homomorphism, and that if E1, E2 are lattice sequential effect algebras, then a bijective morphism φ;E1-E2 is a monomorphism if and only ifφ(a∧b)=φ(a)∧φ(b),(A)a,b∈E1.%研究了效应代数上态射、单调态射和弱单调态射的一些性质,证明了如果E1,E2为格效应代数,φ:E1→E2是1-1态射且φ是格同态,那么φ是单调态射.反之,若φ:E1 →E2是满的单调态射,则φ是格同态.如果E1,E2是格序列效应代数,φ:E1→E2是双射且为态射,那么φ是单调态射当且仅当φ(a∧b)=φ(a)∧φ(b),(V)a,b∈E1.