Exponent reduction for radical Abelian algebras
Let \(A\) be a radical Abelian algebra over a field \(k\), i.e., \(A\) is a crossed product \((K/k,G,\alpha)\) where \(K=k(T)\) is a radical Abelian extension of \(k\), \(T\) is a subgroup of \(K^*\) which is finite modulo \(k^*\) and \(\alpha\in H^2(G,K^*)\) is represented by a cocyle with values in \(T\). Let also \(\mu\) be the group of all roots of unity in an algebraic closure of \(k\). The authors prove that \(K\) contains a primitive root of unity of order \(\exp(A\otimes_k k(\mu))\).
scientific article; zbMATH DE number 1423883