The goal of this paper is to characterize certain coherentlike properties of integral domains in pullback constructions of type □. In one sense, this work is a sequel to that of Brewer and Rutter [BR], in which coherence and several other properties are studied in so-called generalized D + M constructions—that is, pull-backs of type □ in which it is assumed that T = k + M. ([BR] was in turn at least partly inspired by the work of Dobbs and Papick [DP] on coherence in the classical D + M construction, in which T = k + M is assumed to be a valuation domain.) Our work in this more general context is partly motivated by the fact that results which hold for the D + M construction do not always extend to pullbacks of type □. For example, [FG, Thm. 4.2(b)] shows that the characterization of the GCD-property given in [BR, Thm. 11] requires modification, and [FG, Example 4.3] exploits pullbacks to give a counterexample to a conjecture of Anderson and Ryckaert [AR, Question 3.10].
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机译:本文的目的是表征□型回拉构造中积分域的某些相干性质。从某种意义上说,这项工作是布鲁尔和鲁特[BR]的续篇,在布鲁尔和罗特[BR]中,所谓的广义D + M结构研究了相干性和其他一些特性,即,其中□类型的回弹。假设T = k + M。([BR]至少部分是受Dobbs和Papick [DP]关于经典D + M结构中相干性的研究启发的,其中T = k + M被假定为在较一般的情况下,我们的工作部分受以下事实的驱使:D + M结构的结果并不总是扩展到□类型的回撤。例如,[FG,Thm。 4.2(b)]显示了[BR,Thm。]中给出的GCD属性的特征。 [11]需要修改,[FG,示例4.3]利用回撤为Anderson和Ryckaert的猜想提供了反例[AR,问题3.10]。
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