l-Groups with the Unique Pierece's Homomorphism
Xinmin Lu · Journal of Nanchang University · 2010
Pierece proved that,for any distributive lattice L with a minimal element 0,there exists a Pierece's homomorphism f:L→L such that Kerf=0 and f(a)=f(b) in and only if a⊥=b⊥,where a,b∈L and for x∈L,x⊥={y∈L:y∧x=0}.In this note,we discusses the uniqueness of distributive lattice L for Pierece's homomorphism,and prove that if G is an archimedean l-group,then G+ has only one Pierece's homomorphism.