Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Set of $t$-Linked Overrings of an integral domain   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.

6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin