Nagata rings

作     者：Pascual JARA 

作者机构：Department of Algebra University of Granada 18071-Granada Spain 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2015年第10卷第1期

页      面：91-110页

核心收录：

学科分类：1304[艺术学-美术学] 13[艺术学] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by FQM-266 (Junta de Andalucia Research Group) 

主　　题：Cohen-Macaulay Gorenstein Krull Nagata rings 

摘      要：Let A be a commutative ring. For any set P of prime ideals of A, we define a new ring Na（A, P）： the Nagata ring. This new ring has the particularity that we may transform certain properties relative to P to properties on the whole ring Na（A, P）; some of these properties are： ascending chain condition, Krull dimension, Cohen-Macaulay, Gorenstein. Our main aim is to show that most of the above properties relative to a set of prime ideals P（i.e., local properties） determine and are determined by the same properties on the Nagata ring （i.e., global properties）. In order to look for new applications, we show that this construction is functorial, and exhibits a functorial embedding from the localized category （A, P）-Mod into the module category Na（A,P）-Mod.