On bimodules over Noetherian PI rings

Braun, Amiram

doi:10.1090/S0002-9939-09-10125-9

On bimodules over Noetherian PI rings
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Proc. Amer. Math. Soc. 138 (2010), 847-852 Request permission

Abstract:

Let $R$ be a prime Noetherian PI ring, and let $I$ be an ideal in $R$ satisfying $xI \subseteq Ix$ for some $x$ in $R$. We prove that $xI=Ix$. This is obtained as a corollary of a similar more general result, where $I$ can be taken as any finitely generated torsion-free central $R$-bimodule.

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