Suppose $I$ is an ideal in a polynomial ring $R=k[x,y]$. Let $\overline{k}$ be the algebraic closure of $k$ and let $S=\overline{k} [x,y]$. Then is $IS\cap R=I$?
Extension and contraction of ideals in polynomial rings
10
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commutative-algebra
ideals
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0Isn't $R\subset S$ faithfully flat? – 2014-03-02
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0Dear Zuben, could you please accept one of Makoto's answer: he more than deserves it. – 2016-03-13
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0But his/her profile shows "Last seen Nov 23 '11 at 0:58"... – 2017-01-10