Group algebras whose units satisfy a group identity
HTML articles powered by AMS MathViewer
- by Antonio Giambruno, Sudarshan Sehgal and Angela Valenti PDF
- Proc. Amer. Math. Soc. 125 (1997), 629-634 Request permission
Abstract:
Let $FG$ be the group algebra of a torsion group over an infinite field $F$. Let $U$ be the group of units of $FG$. We prove that if $U$ satisfies a group identity, then $FG$ satisfies a polynomial identity. This confirms a conjecture of Brian Hartley.References
- M. Dokuchaev and J. Z. Goncalves, Semigroup identities on units of integral group rings, Glasgow Math. J. (to appear).
- Jairo Zacarias Gonçalves, Free subgroups of units in group rings, Canad. Math. Bull. 27 (1984), no. 3, 309–312. MR 749637, DOI 10.4153/CMB-1984-046-7
- J. Z. Gonçalves and A. Mandel, Semigroup identities on units of group algebras, Arch. Math. (Basel) 57 (1991), no. 6, 539–545. MR 1135408, DOI 10.1007/BF01199058
- A. Giambruno, E. Jespers, and A. Valenti, Group identities on units of rings, Arch. Math. (Basel) 63 (1994), no. 4, 291–296. MR 1290601, DOI 10.1007/BF01189563
- P. Menal, Private letter to B. Hartley, April 6, 1981.
- Donald S. Passman, The algebraic structure of group rings, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977. MR 0470211
- I. Reiner, Maximal orders, London Mathematical Society Monographs, No. 5, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1975. MR 0393100
- Sudarshan K. Sehgal, Topics in group rings, Monographs and Textbooks in Pure and Applied Mathematics, vol. 50, Marcel Dekker, Inc., New York, 1978. MR 508515
- S. K. Sehgal, Units in integral group rings, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 69, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1993. With an appendix by Al Weiss. MR 1242557
- D. S. Warhurst, Topics in Group Rings, Thesis, Manchester, 1981.
Additional Information
- Antonio Giambruno
- Affiliation: Dipartimento di Matematica, Universitá di Palermo, via Archirafi 34, 90123 Palermo, Italy
- MR Author ID: 73185
- ORCID: 0000-0002-3422-2539
- Email: giambruno@ipamat.math.unipa.it, avalenti@ipamat.math.unipa.it
- Sudarshan Sehgal
- Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
- MR Author ID: 158130
- Email: ssehgal@schur.math.ualberta.ca
- Angela Valenti
- Affiliation: Dipartimento di Matematica, Universitá di Palermo, via Archirafi 34, 90123 Palermo, Italy
- Received by editor(s): June 26, 1995
- Additional Notes: Research supported by NR and MURST of Italy and NSERC of Canada.
- Communicated by: Ronald M. Solomon
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 629-634
- MSC (1991): Primary 16S34; Secondary 20C05
- DOI: https://doi.org/10.1090/S0002-9939-97-03581-8
- MathSciNet review: 1350944