Question about modules, quotient rings, and polynomial rings? - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-23T04:44:23Z http://mathoverflow.net/feeds/question/75667 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/75667/question-about-modules-quotient-rings-and-polynomial-rings Question about modules, quotient rings, and polynomial rings? Osiris 2011-09-17T09:44:45Z 2011-09-17T17:16:21Z <p>Consider an integer polynomial ring, $A = \mathbb{Z}[t]$, and a ring of fractions, $B = \mathbb{Z}[t, t^{-1}]$; obviously, $A$ is a subring of $B$.</p> <p>Now we consider two modules over $A$ and $B$, $M$ and $N$. We want to construct a map from $N$ to $M$. But the question is that the two modules are not over the same polynomial ring. So how can we make it?</p> <p>Great thanks!</p> http://mathoverflow.net/questions/75667/question-about-modules-quotient-rings-and-polynomial-rings/75668#75668 Answer by Honghao for Question about modules, quotient rings, and polynomial rings? Honghao 2011-09-17T10:24:21Z 2011-09-17T10:24:21Z <p>I do not think you can map a module over a smaller ring into a module over a larger ring in this case.<code>$\phi(rx)=r\phi(x)$</code> will not satisfy.</p>