Local--Global Properties for Semistar Operations
交换代数
2007-05-23 v1
摘要
We study the "local" behavior of several relevant properties concerning semistar operations, like finite type, stable, spectral, e.a.b. and a.b. We deal with the "global" problem of building a new semistar operation on a given integral domain, by "gluing" a given homogeneous family of semistar operations defined on a set of localizations. We apply these results for studying the local--global behavior of the semistar Nagata ring and the semistar Kronecker function ring. We prove that an integral domain is a Pr{\"u}fer --multiplication domain if and only if all its localizations are Pr{\"u}fer --multiplication domains.
引用
@article{arxiv.math/0305202,
title = {Local--Global Properties for Semistar Operations},
author = {Marco Fontana and Pascual Jara and Eva Santos},
journal= {arXiv preprint arXiv:math/0305202},
year = {2007}
}