An addendum to a Noether Skolem theorem for group-graded rings (Q1115508)

The authors improve the main theorem of [ibid. 113, 483-490 (1988; Zbl 0639.16001)] to the following: Theorem. Let R be a finite dimensional central simple k-algebra that is graded by a finite group G. Assume that R is strongly graded on its support. Then this grading is inner if and only if k is contained in R(1). - The previous version of the theorem needed the assumption of R(1) simple. Then R is a crossed product over R(1), and so is strongly graded.