Norbert Pintye
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 Dec 21 awarded Caucus Sep 11 awarded Critic Aug 23 awarded Necromancer Aug 18 asked Direct image of the exceptional divisor along a blow-up Jul 2 awarded Curious Jun 12 answered Matrices and rank inequality Apr 30 awarded Yearling Apr 30 revised Why does $T(n) \leq 2 T(\lceil \frac{n}{2} \rceil)+\mathcal{O}(n)$ imply $T(n)=\mathcal{O} (n\log(n))$ corrected spelling Apr 30 answered Why does $T(n) \leq 2 T(\lceil \frac{n}{2} \rceil)+\mathcal{O}(n)$ imply $T(n)=\mathcal{O} (n\log(n))$ Apr 30 comment Nilpotent Elements and Intersection of Prime Ideals Where is the problem? The set of nilpotent elements is the radical of $(0)$ (Fact 1), which is the intersection of those prime ideals that contain $(0)$ (Fact 2), that is, the intersection of all prime ideals. At the same time, this immediately implies that the set in question is an ideal. Mind that you need your ring to be commutative with unity. Mar 22 comment Rational roots of polynomials $D(f)$ is the complement of $V(f)$. It is the set of those points where $f$ does not vanish. Mar 22 awarded Revival Mar 21 awarded Informed Mar 19 awarded Cleanup Mar 19 revised Rational roots of polynomials rolled back to a previous revision Mar 18 revised Rational roots of polynomials workaround added Mar 15 comment Rational roots of polynomials I managed to prove that for $n=2$, there is no non-empty open subset of $Y$ contained in $\varphi(X)$. Therefore, the method above does not work. Mar 11 comment Open set in the image of a dominant morphism of affine spaces Indeed. However, we have $\dim(Y\setminus U)\leq 1$ now. Is it possible (though highly unlikely) that we have a bound independently of $n$ in general? Mar 10 comment How to show $\phi(X)$ contains a non-empty open set of its closure $\overline{\phi(X)}$? 'This proof doesn't need $k$ algebraically closed'. It does. Take for example $k=\mathbb{Q}$, $X=Y=\mathbb{A}^1_k$ and $\varphi(x)=x^2$. Then $\varphi$ is dominant, yet its image does not contain any non-empty open. Mar 10 revised Rational roots of polynomials major mistake found