Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585310120180501An equivalence functor between local vector lattices and vector lattices11561405ENKarim BoulabiarDépartement de Mathématiques
Faculté des Sciences de Tunis
Université Tunis-El Manar
Campus UniversitaireJournal Article20171113We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-trivial components. Nevertheless, our main purpose is to prove, via what we call the radical functor, that the category of all vector lattices and lattice homomorphisms is equivalent to the category of local vectors lattices and unital (i.e., unit preserving) lattice homomorphisms.http://cgasa.sbu.ac.ir/article_61405_40f76eb1944c871ec42dac7af3a5fb65.pdf