Let R be a commutative (von
Neumann) regular ring with unit. This paper deals with algebras A over R, and
following standard conventions A will be called a finitely generated R-algebra
whenever A is a finitely generated R-module. One of the principal results obtained is
that all semiprime finitely generated R-algebras are regular rings. Combining this
with a result of J. Wehlen and a theorem of G. Michler and O. Villamayor shows
that the finitely generated semiprime algebras over commutative regular
rings are precisely the semiprime central separable algebras over regular
rings.
