The Burnside problem for semigroups

AbstractWe show that the strong Burnside problem has an affirmative answer for semigroups of finite dimensional matrices over a field. As a corollary of this result and the proof of a theorem of Procesi, it follows that a torsion semigroup embeddable in the multiplicative semigroup of an algebra over a field satisfying a polynomial identity is locally finite. We prove, more generally, that a torsion semigroup of matrices over a skew field all of whose subgroups are locally finite is locally finite