Bézout rings with finite Krull dimension (Q1708240)

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scientific article; zbMATH DE number 6856048
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Bézout rings with finite Krull dimension
scientific article; zbMATH DE number 6856048

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    Bézout rings with finite Krull dimension (English)
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    5 April 2018
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    The main result of this paper is that if \(R\) is a commutative Bézout ring of Krull dimension 1, with stable range 2, then \(R\) is an elementary divisor ring, which generalizes some known results in [\textit{J. W. Brewer} et al., Commun. Algebra 12, 2987--3003 (1984; Zbl 0571.13004)] and [\textit{T. S. Shores}, Proc. Am. Math. Soc. 46, 211--213 (1974; Zbl 0309.13008)].
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    Bézout ring
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    Krull dimension
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    elementary divisor ring
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