I can show that $\mathbb{R}(x)[y]/(x^2+y^2-1)$ is a field, but how do we know it is the smallest field containing $\mathbb{R}[x,y]/(x^2+y^2-1)$? I guess we can define the canonical map. Is there any other way to explain the statement?
2026-03-31 22:08:05.1774994885
The field of fractions of $\mathbb{R}[x,y]/(x^2+y^2-1)$ is $\mathbb{R}(x)[y]/(x^2+y^2-1)$
173 Views Asked by user682705 https://math.techqa.club/user/user682705/detail AtRelated Questions in ABSTRACT-ALGEBRA
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