Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Schemes and morphisms, Centralizing and normalizing extensions, Relevant commutative algebra, Rings with polynomial identity, Zariski's main theorem for P.I. rings, central extension, schemes associated to coherent sheaves of algebras over a scheme, geometric homomorphism, noncommutative schemes, Automorphisms and endomorphisms