Envelopes of commutative rings

被引：0

作者：

Parra, Rafael ^{[1
]}

Saorin, Manuel ^{[1
]}

机构：

[1] Univ Los Andes, Fac Ingn, Escuela Basica, Dept Calculo, Merida, Venezuela

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2012年 / 28卷 / 03期

关键词：

Noetherian ring; envelope; local ring; artinian ring; Krull dimension; MODULES;

D O I：

10.1007/s10114-011-9344-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a significative class F of commutative rings, we study the precise conditions under which a commutative ring R has an F-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.

引用

页码：561 / 580

页数：20

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