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If $a,b,c,d$ are in $R=\mathbb{C}[t]$ and $ad-bc \ne 0$, $L= R(a,b)+R(c,d)$ in $R^{2}$. I want to show that $\dim_{\mathbb{C}}R^{2}/L = \deg(ad-bc)$.
In a previous theorem it was shown that : $\dim_{\mathbb{C}}R /tR = \deg(t)$. So I think of : $\dim_{\mathbb{C}}R^{2}/tR$ and I believe this ...
