2024/10/21 by Gyu Whan Chang, Chang, Gyu Whan, Andreas Reinhart +1 · 1 citation
Decision Sciences · #13A15 #13F05 #13G05 #Commutative Algebra (math.AC) #FOS: Mathematics #Operations Management Techniques
paper · pdf · doi:10.48550/arxiv.2410.16471
openalex publication_date 2024/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An integral domain D is a \em valuation ideal factorization domain (VIFD) if each nonzero principal ideal of D can be written as a finite product of valuation ideals. Clearly, π-domains are VIFDs. We study the ring-theoretic properties of VIFDs and the *-operation analogs of VIFDs. Among them, we show that if D is treed (resp., *-treed), then D is a VIFD (resp., *-VIFD) if and only if D is an \rm h-local Prüfer domain (resp., a *-\rm h-local P*MD) if and only if every nonzero prime ideal of D contains an invertible (resp., a *-invertible) valuation ideal. We also study integral domains D such that for each nonzero nonunit a∈ D, there is a positive integer n such that an can be written as a finite product of valuation elements.