Integral Domains whose Simple Overrings are Intersections of Localizations
交换代数
2007-05-23 v1
摘要
Call a domain an sQQR-domain if each simple overring of , i.e., each ring of the form with in the quotient field of , is an intersection of localizations of . We characterize Pr\"ufer domains as integrally closed sQQR-domains. In the presence of certain finiteness conditions, we show that the sQQR-property is very strong; for instance, a Mori sQQR-domain must be a Dedekind domain. We also show how to construct sQQR-domains which have (non-simple) overrings which are not intersections of localizations.
引用
@article{arxiv.math/0406295,
title = {Integral Domains whose Simple Overrings are Intersections of Localizations},
author = {Marco Fontana and Evan Houston and Thomas Lucas},
journal= {arXiv preprint arXiv:math/0406295},
year = {2007}
}