tensorproduct, p-adic groupring - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T08:23:47Z http://mathoverflow.net/feeds/question/111887 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/111887/tensorproduct-p-adic-groupring tensorproduct, p-adic groupring Gerald N 2012-11-09T10:49:48Z 2012-12-15T16:22:00Z <p>Suppose there is a cyclic group $G$ and a prime $p$. Why can one write</p> <p>$$\mathbb{Z}_p[G] \cong \mathbb{Z}_p \otimes _\mathbb{Z} \mathbb{Z}[G]$$ </p> <p>Is this some theorem which has a name? Thanks for hints.</p> http://mathoverflow.net/questions/111887/tensorproduct-p-adic-groupring/112625#112625 Answer by Simone Virili for tensorproduct, p-adic groupring Simone Virili 2012-11-16T23:49:01Z 2012-11-16T23:49:01Z <p>I do not think this is a research question. Anyway, first of all you should convince yourself that $\mathbb Z_p\otimes_{\mathbb Z} (\mathbb Z[G])\cong(\mathbb Z_p\otimes_{\mathbb Z} \mathbb Z)[G]$. After this I think you will have no difficulty in verifying that $\mathbb Z_p\otimes_{\mathbb Z} \mathbb Z\cong \mathbb Z_p$. </p> <p>This is more an exercise than a theorem so it has no specific name. Anyway, similar operations are usually called "extensions of scalars". </p>