Abstract

In this paper we show that every central simple algebra A over Q_p, generated by a multiplicative semigroup S ⊂ A with the property that the minimal polynomial of every element in S splits over Q_p, is isomorphic to M_n(Q_p). If, in addition, S ⊂ A^* is a compact group, then it contains a commutative normal subgroup of finite index.

Authors