Generalised Tits alternative for linear semigroups (Q1903683)

The authors prove the following interesting generalization of the Tits alternative: If \(S\) is a subsemigroup of a semigroup \(M(n,k)\) of the matrices of size \(n\) over a field \(K\) and \(K\) is finitely generated then \(S\) has no free non-commutative subsemigroup if and only if \(S\) satisfies a semigroup identity. Several other more technical equivalent conditions are also given.