Abstract
Let G be a monoid with unity e and cancellation, let ℱ be a commutative ring with 1, and let be a G-graded ℱ-semiprime algebra with finite G-grading satisfying a G-graded generalized polynomial identity (with an antiautomorphism when G is commutative) over ℛ
e
. If ℛ
e
is prime, then ℛ has a strict GPI over ℛ
e
.
ACKNOWLEDGMENT
The authors would like to express their sincere thanks to the referee for presenting a reasonable suggestion on the definition of graded generalized polynomial identities and pointing out several misprints.
Notes
Communicated by M. Bresar.