two polynomials - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T06:33:36Z http://mathoverflow.net/feeds/question/77218 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/77218/two-polynomials two polynomials filipm 2011-10-05T09:52:36Z 2011-10-05T15:50:08Z <p>If $p,q:\mathbb R^3\rightarrow\mathbb R$ are two polynomials, such that <code>$\{p=0\}\cap\{q=0\}$</code> is two-dimensional, does it follow that $p$ and $q$ have a common factor? (I believe it does.) How to prove that? </p> http://mathoverflow.net/questions/77218/two-polynomials/77249#77249 Answer by Pham Hung Quy for two polynomials Pham Hung Quy 2011-10-05T15:50:08Z 2011-10-05T15:50:08Z <p>Here is my answer. We consider the rimg $A=R[x,y,z]$ , $dimA=3$. We have $V((p))∩V((q))=V((p,q))$. If $gcd(p,q)=1$, then $ht(p,q)=2$. So $V((p))∩V((q))))=V((p,q))$ is not 2-dimension. </p>