Su un particolare modulo di frazioni di certi Λ-moduli

Abstract

It is well known that an unique factorization domain is a Krull domain (see [1]).In the light of this result we espound in this paper some considerations on Λ-modules from which it follows that if $M (+,*)$ is a torsion-free f-cryptofactorial Λ-module and if $Λ-{0}(·)$ is a h-finite semigroup for which any atomic element is prime, then $M(+,*)$ is included in a quasi Krull module is a Krull module in the particular case of $Λ(·)$ f-cryptofactorial semigroup (see definitions below).By this we have that the factorial modules (see [2]) are Krull modules and therefore such are also the direct sum and the direct product of factorial modules, the free modules and the projective modules over an U.F.D.To conclude we notice that any cryptofactorial domain is included in a U.F.D.