Group algebras with units

satisfying a group identity

Author:
Chia-Hsin Liu

Journal:
Proc. Amer. Math. Soc. **127** (1999), 327-336

MSC (1991):
Primary 16S34

DOI:
https://doi.org/10.1090/S0002-9939-99-04744-9

MathSciNet review:
1487322

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be the group algebra of a group over a field , and let be its group of units. A conjecture by Brian Hartley asserts that if is a torsion group and satisfies a group identity, then satisfies a polynomial identity. This was verified earlier in case is an infinite field. Here we modify the original proof so that it handles fields of all sizes.

**[BRT]**Y. Billig, D. Riley, and V. Tasi\'{c},*Non-matrix varieties and nil-generated algebras whose units satisfy a group identity*, J. Algebra**190**(1997), no. 1, 241-252. CMP**97:10****[GJV94]**A. Giambruno, E. Jespers, and A. Valenti,*Group identities on units of rings*, Arch. Math. (Basel)**63**(1994), no. 4, 291-296. MR**95h:16044****[GM91]**J. Z. Gonçalves and A. Mandel,*Semigroup identities on units of group algebras*, Arch. Math. (Basel)**57**(1991), no. 6, 539-545. MR**93g:16049****[Gon84]**J. Z. Gonçalves,*Free subgroups of units in group rings*, Canad. Math. Bull.**27**(1984), no. 3, 309-312. MR**85k:20021****[GSV]**A. Giambruno, S. Sehgal, and A. Valenti,*Group algebras whose units satisfy a group identity*, Proc. Amer. Math. Soc.**125**(1997), 629-634. MR**97f:16056****[Kar89]**G. Karpilovsky,*Unit groups of group rings*, Longman Scientific & Technical, 1989. MR**91h:16001****[Pas]**D. S. Passman,*Group algebras whose units satisfy a group identity II*, Proc. Amer. Math. Soc.**125**(1997), no. 3, 657-662. MR**98c:16033****[Pas85]**D. S. Passman,*The algebraic structure of group rings*, Robert E. Krieger, 1985. MR**86j:16001****[YC96]**Chi-Tsuen Yeh and Chen-Lian Chuang,*Nil polynomials of prime rings*, J. Algebra**186**(1996), no. 3, 781-792. MR**97k:16031**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
16S34

Retrieve articles in all journals with MSC (1991): 16S34

Additional Information

**Chia-Hsin Liu**

Affiliation:
Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706

Email:
chliu@math.wisc.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-04744-9

Received by editor(s):
March 25, 1997

Received by editor(s) in revised form:
September 29, 1997

Communicated by:
Ken Goodearl

Article copyright:
© Copyright 1999
American Mathematical Society