a noncommutative analogue of a cyclotomic field extension in the realm of central simple algebras is a schur algebra, namely a finite dimensional central simple algebra $a$ over a field $k$ which is generated over $k$ by a finite subgroup of the multiplicative group of $a$. its projective version, a projective schur algebra, is the noncommutative analogue of a radical field extension, namely a finite dimensional central simple algebra $a$ over a field $k$ which is generated over $k$ by a subgroup $g$ of the multiplicative group of $a$ such that $g/k*$ is finite. the talk will focus on projective schur algebras and the subgroup of the brauer group that they determine.