Abstract
Let G be a monoid with cancellation and let ℛ be a strongly G-graded algebra with finite G-grading satisfying a graded polynomial identity. We show that ℛ is a PI algebra.
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Acknowledgments
We express our gratitude to Prof. M.V. Zaicev for bringing to our attention his joint paper Bahturin and Zaicev (Citation1998) with Prof. Yu. A. Bahturin. We are also grateful to the referee for his/her useful comments.