A Noether Skolem theorem for group-graded rings

James Osterburg; Declan Quinn

doi:10.1016/0021-8693(88)90174-3

A Noether Skolem theorem for group-graded rings

James Osterburg, Declan Quinn

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

The classical Noether Skolem theorem gives conditions to determine if an automorphism or a derivation of a finite-dimensional central simple algebra is inner. The definition of inner has been extended to more general Hopf algebra actions. In this paper, we study group-gradings of central simple algebras and we give sufficient conditions for the grading to be inner. This provides a partial answer to a question of J. Bergen and S. Montgomery.

Original language	English (US)
Pages (from-to)	483-490
Number of pages	8
Journal	Journal of Algebra
Volume	113
Issue number	2
DOIs	https://doi.org/10.1016/0021-8693(88)90174-3
State	Published - Mar 1988
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/0021-8693(88)90174-3

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abstract = "The classical Noether Skolem theorem gives conditions to determine if an automorphism or a derivation of a finite-dimensional central simple algebra is inner. The definition of inner has been extended to more general Hopf algebra actions. In this paper, we study group-gradings of central simple algebras and we give sufficient conditions for the grading to be inner. This provides a partial answer to a question of J. Bergen and S. Montgomery.",

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AB - The classical Noether Skolem theorem gives conditions to determine if an automorphism or a derivation of a finite-dimensional central simple algebra is inner. The definition of inner has been extended to more general Hopf algebra actions. In this paper, we study group-gradings of central simple algebras and we give sufficient conditions for the grading to be inner. This provides a partial answer to a question of J. Bergen and S. Montgomery.

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A Noether Skolem theorem for group-graded rings

Abstract

ASJC Scopus subject areas

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