Envelopes of Commutative Rings

作     者：Rafael PARRA Manuel SAORIN 

作者机构：Departamento de Clculo. Escuela Bsica Facultad de Ingeniería Universidad de los Andes Departamento de Matemticas Universidad de Murcia 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2012年第28卷第3期

页      面：561-580页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 0822[工学-轻工技术与工程] 0701[理学-数学] 

基　　金：supported by research projects from the Fundación ‘Sneca’ of Murcia (Programa de Ayudas a Grupos de Excelencia) the Spanish Ministry of Science and Innovation (Programa Nacional de Proyectos de Investigación Fundamental), with a part of FEDER funds 

主　　题：Noetherian ring envelope local ring artinian ring Krull dimension 

摘      要：Given a significative class F of commutative rings, we study the precise conditions under which a commutative ring R has an S-envelope. A full answer is obtained when F is the class of fields, semisimple commutative rings or integral domains. When .F is the class of Noetherian rings, we give a full answer when the Krull dimension of R is zero and when the envelope is required to be epimorphic. The general problem is reduced to identifying the class of non-Noetherian rings having a monomorphic Noetherian envelope, which we conjecture is the empty class.