Testing isomorphism of finitely generated algebras - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T00:15:26Z http://mathoverflow.net/feeds/question/99150 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/99150/testing-isomorphism-of-finitely-generated-algebras Testing isomorphism of finitely generated algebras Hugo Chapdelaine 2012-06-08T21:50:46Z 2012-06-09T02:46:04Z <p>Let $A=\mathbf{Q}[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over the rational numbers. Let $B=\mathbf{Q}[f_1,\ldots,f_r]$ and $C=\mathbf{Q}[g_1,\ldots,g_s]$ be two <strong>finitely generated</strong> $\mathbf{Q}$-subalgebras of $A$ with explicit generators. </p> <p>Q1: Is there a finite time (efficient) algorithm that allows one to say when is $B\simeq C$ as $\mathbf{Q}$-algebra?</p> <p>Q2: Is there a finite time (efficient) algorithm that allows one to say when is $Frac(B)\simeq Frac(C)$?</p> <p>Here $Frac(B)$ denotes the fraction field. In both questions I really mean <strong>isomorphic</strong> and not equal.</p>