Graded Generalized Polynomial Identities (with an Antiautomorphism) in Graded Algebras

Abstract

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 . Key Words: Generalized polynomial identityGraded algebraGraded generalized polynomial identityPrime algebraSemiprime algebra2010 Mathematics Subject Classification: 16W5016R2016R5016N60 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.