通过扭转模对射影模的无扭转扩展

Pub Date : 2023-03-01 DOI:10.1216/jca.2023.15.31
L. Fuchs
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引用次数: 1

摘要

本文将P. Griffith[12]提出的一个关于阿贝群的问题推广到积分域上的模,并证明了M. Dugas和J. Irwin[2]的一个定理的类比。具有以下性质的扭转模T被刻画:如果M是无扭转模,F是一个射影子模,使得M/F ~ = T,则M是射影子模(定理4.1)。定理6.4表明,对于基数不与ω余的阿贝群,这等价于L. Fuchs和K. Rangaswamy[9]意义上的完全约简。讨论了评价域的问题,结果与阿贝尔群的情况类似。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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TORSION-FREE EXTENSIONS OF PROJECTIVE MODULES BY TORSION MODULES
We consider a generalization of a problem raised by P. Griffith [12] on abelian groups to modules over integral domains, and prove an analogue of a theorem of M. Dugas and J. Irwin [2]. Torsion modules T with the following property are characterized: if M is a torsion-free module and F is a projective submodule such that M/F ∼= T , then M is projective (Theorem 4.1). It is shown in Theorem 6.4 that for abelian groups whose cardinality is not cofinal with ω this is equivalent to being totally reduced in the sense of L. Fuchs and K. Rangaswamy [9]. The problem for valuation domains is also discussed, the results are similar to the case of abelian groups.
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