Abstract
It is known that a Prüfer domain either with dimension 1 or with finite character has the stacked bases property. Following Brewer and Klinger, some rings of integer-valued polynomials provide, for every n ≥ 2, examples of n-dimensional Prüfer domains without finite character which have the stacked bases property. But, the following question is still open: does the two-dimensional Prüfer domain \({{\rm Int}(\mathbb {Z})=\{f \in \mathbb {Q}[X]\mid f(\mathbb {Z})\subseteq \mathbb {Z}\}}\) have the stacked bases property? By means of the UCS-property, we reduce the question to the search for some 2 × 2 matrices with coefficients in \({{\rm Int}(\mathbb{Z})}\) .
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Chabert, JL. Does Int \({(\mathbb {Z})}\) have the stacked bases property?. Arab. J. Math. 1, 47–52 (2012). https://doi.org/10.1007/s40065-012-0021-6
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DOI: https://doi.org/10.1007/s40065-012-0021-6