Roots of unity in algebraic K-theory - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T23:28:29Z http://mathoverflow.net/feeds/question/99032 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/99032/roots-of-unity-in-algebraic-k-theory Roots of unity in algebraic K-theory Craig Westerland 2012-06-07T12:20:22Z 2012-06-07T12:20:22Z <p>For any commutative ring $R$, the tensor product of (finitely generated, projective) $R$-modules equips the algebraic K-theory $K(R) = K_0(R)$ with the structure of a commutative ring with unit.</p> <p>For $n>2$, I'm wondering what assumptions one might need to impose upon $R$ to ensure that $K(R)$ contains primitive $n^{\rm th}$ roots of unity (i.e., a cyclic subgroup of $K(R)^{\times}$ of order $n$). I'd even be happy with a good family of examples.</p>