Fractionary fuzzy ideals and Dedekind domains
This paper continues the investigation of the previously introduced notions of fractionary fuzzy ideals (a special fuzzy \(R\)-submodule of the quotient field of an integral domain \(R\)) and fuzzy invertible fractionary fuzzy ideals. It is shown that a finite-valued fractionary fuzzy ideal of an integral domain \(R\) with invertible level ideals has a finite minimal generating set. Moreover the authors give three characterizations of a Dedekind domain in terms of factorization of fuzzy ideals as products of prime fuzzy ideals as well as in terms of invertibility of some special fractionary fuzzy ideals. Finally some results are given concerning the factorization of fractionary fuzzy ideals.
scientific article; zbMATH DE number 1398907