sub ring of algebra over subfield - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T23:40:53Z http://mathoverflow.net/feeds/question/69649 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/69649/sub-ring-of-algebra-over-subfield sub ring of algebra over subfield ventura 2011-07-06T17:23:25Z 2011-10-26T23:22:12Z <p>Let $k$ be a field and $k[a]$ an algebric extension. If $A$ is a reduced commutative algebra over $k[a]$ and $B$ is a subring which is an algebra over $k$, then is the following true: if there exist elements $x,y\in B$ such that $xa+y=0$ then $x=y=0$?</p> <p>If it is not true in the general case, is it true in the case where $k[a]$ is an inseparable extension of degree $p$ over $k$, $A$ is finitely generated, and $B=A^{p}=\{{y^{p}\ |\ y\in A\}}$?</p> http://mathoverflow.net/questions/69649/sub-ring-of-algebra-over-subfield/69652#69652 Answer by ventura for sub ring of algebra over subfield ventura 2011-07-06T18:20:30Z 2011-07-06T19:09:08Z <p>im sorry i ment to write $x,y\in B$ i hope now its clear. $a\notin B$ thanks for the editing</p>