Uppers to zero in polynomial rings and Prüfer-like domains
| dc.creator | Chang, Gyu Whan | |
| dc.creator | Fontana, Marco | |
| dc.date | 2008-01-10 | |
| dc.date.accessioned | 2026-07-07T08:53:41Z | |
| dc.date.available | 2026-07-07T08:53:41Z | |
| dc.description | 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 $g \in D[X]$ with content $\co_D(g) = D$; (b) an upper to zero $Q$ in $D[X]$ is a maximal $t$-ideal if and only if $Q$ contains a nonzero polynomial $g \in D[X]$ with $\co_D(g)^v = D$. Using these facts, the notions of UM$t$-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 $\star$ in the sense of Okabe-Matsuda, we introduce the $\star$-quasi-Prüfer domains. We give several characterizations of these domains and we investigate their relations with the UM$t$-domains and the Prüfer $v$-multiplication domains. | |
| dc.identifier | https://arxiv.org/abs/0801.1632 | |
| dc.identifier | http://arxiv.org/abs/0801.1632 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145707 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13F05; 13A15; 13G05; 13B25 | |
| dc.title | Uppers to zero in polynomial rings and Prüfer-like domains | |
| dc.type | text |