On bimodules over Noetherian PI rings
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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.References
- Amiram Braun and Charudata R. Hajarnavis, Generator ideals in Noetherian PI rings, J. Algebra 247 (2002), no. 1, 134–152. MR 1873387, DOI 10.1006/jabr.2001.8959
- Amiram Braun and Nikolaus Vonessen, Integrality for PI-rings, J. Algebra 151 (1992), no. 1, 39–79. MR 1182014, DOI 10.1016/0021-8693(92)90131-5
- Amiram Braun and Robert B. Warfield Jr., Symmetry and localization in Noetherian prime PI rings, J. Algebra 118 (1988), no. 2, 322–335. MR 969675, DOI 10.1016/0021-8693(88)90024-5
- P. M. Cohn, Algebra. Vol. 3, 2nd ed., John Wiley & Sons, Ltd., Chichester, 1991. MR 1098018
- Barbara Cortzen and Lance W. Small, Finite extensions of rings, Proc. Amer. Math. Soc. 103 (1988), no. 4, 1058–1062. MR 954983, DOI 10.1090/S0002-9939-1988-0954983-6
- A. Fröhlich, I. Reiner, and S. Ullom, Class groups and Picard groups of orders, Proc. London Math. Soc. (3) 29 (1974), 405–434. MR 357464, DOI 10.1112/plms/s3-29.3.405
- K. R. Goodearl and R. B. Warfield Jr., An introduction to noncommutative Noetherian rings, London Mathematical Society Student Texts, vol. 16, Cambridge University Press, Cambridge, 1989. MR 1020298
- Robert M. Guralnick, J. Chris Robson, and Lance W. Small, Normalizing elements in PI rings, Proc. Amer. Math. Soc. 123 (1995), no. 6, 1955–1957. MR 1301026, DOI 10.1090/S0002-9939-1995-1301026-4
- J. C. McConnell and J. C. Robson, Noncommutative Noetherian rings, Pure and Applied Mathematics (New York), John Wiley & Sons, Ltd., Chichester, 1987. With the cooperation of L. W. Small; A Wiley-Interscience Publication. MR 934572
- S. Montgomery, A generalized Picard group for prime rings, Topics in algebra, Part 1 (Warsaw, 1988) Banach Center Publ., vol. 26, PWN, Warsaw, 1990, pp. 55–63. MR 1171225
- Louis H. Rowen, Ring theory, Student edition, Academic Press, Inc., Boston, MA, 1991. MR 1095047
- Wolmer V. Vasconcelos, On quasi-local regular algebras, Symposia Mathematica, Vol. XI (Convegno di Algebra Commutativa, INDAM, Rome, 1971) Academic Press, London, 1973, pp. 11–22. MR 0330159
Additional Information
- Amiram Braun
- Affiliation: Department of Mathematics, University of Haifa, Haifa, Israel 31905
- Email: abraun@math.haifa.ac.il
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 847-852
- MSC (2000): Primary 16P40, 16R20; Secondary 16N20, 16D20
- DOI: https://doi.org/10.1090/S0002-9939-09-10125-9
- MathSciNet review: 2566550