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 Oct8 awarded Yearling Jul2 awarded Curious Apr14 accepted Algebraic closure of a subfield of the field of fraction of a variety Apr14 comment Algebraic closure of a subfield of the field of fraction of a variety Thank you for sharing the link. I wonder if there is some classical book where this proof is written down. Apr14 asked Algebraic closure of a subfield of the field of fraction of a variety Apr9 accepted Nice exercises on resultants Apr7 comment Nice exercises on resultants Thank you for these references! Apr3 accepted If $A/\mathfrak a$ is flat over $A$ then $V(\mathfrak a)$ is open. Why? Apr2 awarded Promoter Apr2 revised Nice exercises on resultants added 87 characters in body Apr2 comment If $A/\mathfrak a$ is flat over $A$ then $V(\mathfrak a)$ is open. Why? I would like to ask you one more question. If $A$ is any ring, and $M$ is any module over $A$, is it correct that $\text{Supp}(M)$ is a closed subset of $\text{Spec}(A)$? If not, would could you please give me an example? Apr2 accepted Is it true that an ideal is primary iff its radical is prime? Apr1 comment If $A/\mathfrak a$ is flat over $A$ then $V(\mathfrak a)$ is open. Why? Thank you for this answer! Could you please tell me the definition of $\text{Supp}$? In particular, what is $\text{Supp}(I)$? Apr1 comment Is it true that an ideal is primary iff its radical is prime? Despite the down vote I like this question, and hope the example provided below might be helpful for someone :) Apr1 comment If $A/\mathfrak a$ is flat over $A$ then $V(\mathfrak a)$ is open. Why? Cantlog, thanks a lot for your comment! Indeed $A$ is noetherian in Milne, so I changed the question and the link you gave answers this question completely. Apr1 revised If $A/\mathfrak a$ is flat over $A$ then $V(\mathfrak a)$ is open. Why? edited tags; improved formatting Apr1 comment If $A/\mathfrak a$ is flat over $A$ then $V(\mathfrak a)$ is open. Why? Thank you for this comment. This statement is given in a footnote on page 42 of Milne's "Primer in commutative algebra" jmilne.org/math/xnotes/ca.html , version version 3.00, May 2, 2013. Since Milne states this without any explanation I still believe that this should not be too hard... Apr1 comment A gentle reference for flat modules with exercises Thank you for this recommendation, I will have a look Apr1 asked A gentle reference for flat modules with exercises Apr1 comment Complexifications of degree 3 subschemes in $\mathbb A^2_{\mathbb R}$ Thank you for this answer! I guess this means indeed that there is a mistake in this exercise. Maybe it is worth to write to the authors of this book...