Group rings satisfying a polynomial identity. III
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- by D. S. Passman
- Proc. Amer. Math. Soc. 31 (1972), 87-90
- DOI: https://doi.org/10.1090/S0002-9939-1972-0289671-3
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Abstract:
Let $K[G]$ denote the group ring of $G$ over the field $K$ and let $\Delta$ denote the F.C. subgroup of $G$. In this paper we show that if $K[G]$ satisfies a polynomial identity of degree $n$, then $[G:\Delta ] \leqq n/2$. Moreover this bound is best possible.References
- D. S. Passman, Linear identities in group rings. I, II, Pacific J. Math. 36 (1971), 457–483; ibid. 36 (1971), 485–505. MR 0283100, DOI 10.2140/pjm.1971.36.485
- Donald S. Passman, Infinite group rings, Pure and Applied Mathematics, vol. 6, Marcel Dekker, Inc., New York, 1971. MR 0314951
- D. S. Passman, Group rings satisfying a polynomial identity, J. Algebra 20 (1972), 103–117. MR 285631, DOI 10.1016/0021-8693(72)90091-9
- Martha Smith, On group algebras, Bull. Amer. Math. Soc. 76 (1970), 780–782. MR 258987, DOI 10.1090/S0002-9904-1970-12549-6
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 87-90
- DOI: https://doi.org/10.1090/S0002-9939-1972-0289671-3
- MathSciNet review: 0289671