Proceedings of the American Mathematical Society

Author(s): Robert L. Snider
Journal: Proc. Amer. Math. Soc. 124 (1996), 1043-1049.
MSC (1991): Primary 16S34, 20C05; Secondary 16K20, 16S50
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 16S34, 20C05, 16K20, 16S50

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

DOI: 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
Copyright of article: Copyright 1996, American Mathematical Society

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