The smallest closed subcategory containing the μcomplemented modules
作者:
Ana M. de Viola-Prioli,
Jorge E. Viola-Prioli,
期刊:
Communications in Algebra
(Taylor Available online 2000)
卷期:
Volume 28,
issue 10
页码: 4971-4980
ISSN:0092-7872
年代: 2000
DOI:10.1080/00927870008827134
出版商: Gordon and Breach Science Publishers Ltd.
数据来源: Taylor
摘要:
Given a hereditary torsion functor , the class of μ-complemented modules was recently introduced by P.F. Smith and the authors as an analogue of extending modules. This current article explores this class by viewing it as a subclass ofEX, the smallest closed subcategory which contains it. As a consequence the class of μ-complemented modules is shown here to be closed under the formation of module of quotients. As toEX, we prove that it is closed under arbitrary direct products in Mod-RifRis a valuation ring. On the other hand, ifRis commutative Noetherian and μ is jansian then every μ-complemented module is a direct sum of a μ-torsion module and a semisimple, which prompted us to analyze whenEXcontains a subgenerator of this form.
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