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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On bimodules over Noetherian PI rings


Author: Amiram Braun
Journal: Proc. Amer. Math. Soc. 138 (2010), 847-852
MSC (2000): Primary 16P40, 16R20; Secondary 16N20, 16D20
Published electronically: October 22, 2009
MathSciNet review: 2566550
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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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Additional Information

Amiram Braun
Affiliation: Department of Mathematics, University of Haifa, Haifa, Israel 31905
Email: abraun@math.haifa.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10125-9
PII: S 0002-9939(09)10125-9
Received by editor(s): April 18, 2009
Received by editor(s) in revised form: June 23, 2009, and July 19, 2009
Published electronically: October 22, 2009
Communicated by: Martin Lorenz
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.