Some patching results on algebras over two-dimensional factorial domains

摘要

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=A _x∩A _y where A _x and A _y are polynomial algebras in one variable over R _x and R _y 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.