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

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 identity
• Graded algebra
• Graded generalized polynomial identity
• Prime algebra
• Semiprime algebra

2010 Mathematics Subject Classification:

• 16W50
• 16R20
• 16R50
• 16N60

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.