A theorem on artinian rings
作者:
Jinzhong Xu,
期刊:
Communications in Algebra
(Taylor Available online 1994)
卷期:
Volume 22,
issue 3
页码: 905-914
ISSN:0092-7872
年代: 1994
DOI:10.1080/00927879408824884
出版商: Marcel Dekker, Inc.
关键词: nonzero flat preenvelopes;Artinian rings;13C05;13C11
数据来源: Taylor
摘要:
In this short paper, we prove that a commutative Noetherian ring R is Artinian if and only if for any nonzero R-module M there is a nonzero linear map from M into F with F flat and if and only if there is a nonzero linear map from M into P with P projective. An example will show that this is not true for noncommutative rings. The motivation of the present discussion is partially from [I] where flat envelopes of modules were studied. It is also motivated by the study of embeddings of modules into projective modules.
点击下载:
PDF (266KB)
返 回