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

 

Endomorphism rings of simple modules
over group rings


Author: Robert L. Snider
Journal: Proc. Amer. Math. Soc. 124 (1996), 1043-1049
MSC (1991): Primary 16S34, 20C05; Secondary 16K20, 16S50
MathSciNet review: 1327044
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Abstract: If $N$ is a finitely generated nilpotent group which is not abelian-by-finite, $k$ a field, and $D$ a finite dimensional separable division algebra over $k$, then there exists a simple module $M$ for the group ring $k[G]$ with endomorphism ring $D$. An example is given to show that this cannot be extended to polycyclic groups.


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Additional Information

Robert L. Snider
Affiliation: Department of Mathematics Virginia Tech Blacksburg, Virginia 24061-0123
Email: snider@math.vt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03368-0
PII: S 0002-9939(96)03368-0
Keywords: Group ring, endomorphism ring, division ring
Received by editor(s): October 17, 1994
Communicated by: Ken Goodearl
Article copyright: © Copyright 1996 American Mathematical Society