Tiberiu Dumitrescu and Cristodor Ionescu: Some examples of two-dimensional regular rings, p.271-277

Abstract:

Let $B$ be a ring and $A=B[X,Y]/(aX^2+bXY+cY^2-1)$ where $a,b,c\in B$. We study the smoothness of $A$ over $B$ and the regularity of $A$ when $B$ is a ring of algebraic integers.

Key Words: Smooth algebra, regular ring, ring of algebraic integers.

2000 Mathematics Subject Classification: Primary: 13H05;
Secondary: 13F05, 11R04.

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