Hereditary finitely generated algebras satisfying a polynomial identity

Abstract:

If $\Lambda$ is a right and left p.p. ring which satisfies a polynomial identity and is a finitely generated algebra over its center, then $\Lambda \simeq \Gamma \times \Omega$, where $\Gamma$ is a semiprime ring having a von Neumann regular classical quotient ring which is module-finite over its center and $\Omega$ has nonzero prime radical at each of its Pierce stalks. If $\Lambda$ is right and left hereditary, then $\Gamma$ is an order over a commutative hereditary ring in the sense of [7]; the ring $\Omega$ is then a direct product of finitely many indecomposable piecewise domains.