Some patching results on algebras over two-dimensional factorial domains

Dutta, Amartya K. ; Gupta, Neena ; Onoda, Nobuharu (2012) Some patching results on algebras over two-dimensional factorial domains Journal of Pure and Applied Algebra, 216 (7). pp. 1667-1679. ISSN 0022-4049

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Official URL: http://doi.org/10.1016/j.jpaa.2012.01.009

Related URL: http://dx.doi.org/10.1016/j.jpaa.2012.01.009

Abstract

Let R = k[x, y] be the polynomial ring in two variables over a field k. We investigate the structure and properties of R-algebras A which are obtained as A = Ax ∩ Ay where Ax and Ay are polynomial algebras in one variable over Rx and Ry respectively. Most of our results hold when R is a two-dimensional UFD and x, y is an R-regular sequence generating a maximal ideal of R

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