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arXiv · 1610.03977

G-Graded Central Polynomials and G-Graded Posner's Theorem

Yakov Karasik
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Abstract

Let F be characteristic zero field, G a residually finite group and W a G-prime and PI F-algebra. By constructing G-graded central polynomials for W, we prove the G-graded version of Posner's theorem. More precisely, if S denotes all non-zero degree e central elements of W, the algebra S^{-1}W is G-graded simple and finite dimensional over its center. Furthermore, we show how to use this theorem in order to recapture the result of Aljadeff and Haile stating that two G-simple algebras of finite dimension are isomorphix iff their ideals of graded identities coincide.

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Yakov Karasik. 2016-10-13. G-Graded Central Polynomials and G-Graded Posner's Theorem. https://arxiv.org/abs/1610.03977

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