效应代数上态射的一些性质

Some properties of morphisms of effect algebras

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,:E1→E2是1-1态射且是格同态,那么是单调态射.反之,若:E1→E2是满的单调态射,则是格同态。如果E1,E2是格序列效应代数,:E1→E2是双射且为态射,那么是单调态射当且仅当(a∧b)=(a)∧(b),a,b∈E1.

Some properties of morphisms of effect algebras,morphism,monomorphisms and weak monomorphisms are discussed.It is proved that if E1,E2 are lattice effect algebras and Ф：E1→E2 is an injective morphism and a lattice homomorphism,then  is a monomorphism;conversely,a surjective monomorphism Ф：E1→E2 must be a lattice homomorphism,and that if E1,E2 are lattice sequential effect algebras,then a bijective morphism Ф：E1→E2 is a monomorphism if and only if Ф（a∧b）=Ф（a）∧Ф（b）,a,b∈E1.