2008/01/10 by Gyu Whan Chang, Chang, Gyu Whan, Marco Fontana +1
Mathematics · #13A15 #13B25 #13F05 #13G05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13A15 #msc:13B25 #msc:13F05 #msc:13G05
paper · pdf · doi:10.48550/arxiv.0801.1632
arxiv created 2008/01/10 · arxiv updated 2009/12/01
Let D be an integral domain and X an indeterminate over D. It is well known that (a) D is quasi-Prüfer (i.e, its integral closure is a Prüfer domain) if and only if each upper to zero Q in D[X] contains a polynomial g ∈ D[X] with content \coD(g) = D; (b) an upper to zero Q in D[X] is a maximal t-ideal if and only if Q contains a nonzero polynomial g ∈ D[X] with \coD(g)v = D. Using these facts, the notions of UMt-domain (i.e., an integral domain such that each upper to zero is a maximal t-ideal) and quasi-Prüfer domain can be naturally extended to the semistar operation setting and studied in a unified frame. In this paper, given a semistar operation ⋆ in the sense of Okabe-Matsuda, we introduce the ⋆-quasi-Prüfer domains. We give several characterizations of these domains and we investigate their relations with the UMt-domains and the Prüfer v-multiplication domains.