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Coordinates in two variables over a $\mathbb {Q}$-algebra

Coordinates in two variables over a $\mathbb {Q}$-algebra

This paper studies coordinates in two variables over a $\mathbb {Q}$-algebra. It gives several ways to characterize such coordinates. Also, various results about coordinates in two variables that were previously only known for fields, are extended to arbitrary $\mathbb {Q}$-algebras.