On the Set of $t$-Linked Overrings of an integral domain
| dc.creator | Mimouni, Abdeslam | |
| dc.date | 2006-11-18 | |
| dc.date | 2007-11-15 | |
| dc.date.accessioned | 2026-07-07T08:43:01Z | |
| dc.date.available | 2026-07-07T08:43:01Z | |
| dc.description | et $R$ be an integral domain with quotient field $L$. An overring $T$ of $R$ is $t$-linked over $R$ if $I^{-1}=R$ implies that $(T:IT)=T$ for each finitely generated ideal $I$ of $R$. Let $O_{t}(R)$ denotes the set of all $t$-linked overrings of $R$ and $O(R)$ the set of all overrings of $R$. The purpose of this paper is to study some finiteness conditions on the set $O_{t}(R)$. Particularly, we prove that if $O_{t}(R)$ is finite, then so is $O(R)$ and $O_{t}(R)=O(R)$, and if each chain of $t$-linked overrings of $R$ is finite, then each chain of overrings of $R$ is finite. This yields that the $t$-linked approach is more efficient than the Gilmer's treatment in \cite{G1}. We also examine the finiteness conditions in some Noetherian-like settings such as Mori domain, quasicoherent Mori domain, Krull domain etc. We establish a connection between $O_{t}(R)$ and the set of all strongly divisorial ideals of $R$ and we conclude by a characterization of domains $R$ that are $t$-linked under all their overrings. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611556 | |
| dc.identifier | http://arxiv.org/abs/math/0611556 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142169 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13G05, 13F05 (Primary); 13B02, 13B22 (Secondary) | |
| dc.title | On the Set of $t$-Linked Overrings of an integral domain | |
| dc.type | text |