Vol. 66, No. 1, 1976

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On semiprime P.I.-algebras over commutative regular rings

Efraim Pacillas Armendariz

Vol. 66 (1976), No. 1, 23–28

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.

Mathematical Subject Classification
Primary: 16A30, 16A30
Received: 14 October 1975
Revised: 1 April 1976
Published: 1 September 1976
Efraim Pacillas Armendariz