Group algebras whose simple modules are injective
HTML articles powered by AMS MathViewer
- by Daniel R. Farkas and Robert L. Snider
- Trans. Amer. Math. Soc. 194 (1974), 241-248
- DOI: https://doi.org/10.1090/S0002-9947-1974-0357475-5
- PDF | Request permission
Abstract:
Let F be either a field of char 0 with all roots of unity or a field of char $p > 0$. Let G be a countable group. Then all simple $F[G]$-modules are injective if and only if G is locally finite with no elements of order char F and G has an abelian subgroup of finite index.References
- Richard Brauer, On the representation of a group of order $g$ in the field of the $g$-th roots of unity, Amer. J. Math. 67 (1945), 461–471. MR 14085, DOI 10.2307/2371973
- Edward Formanek and Robert L. Snider, Primitive group rings, Proc. Amer. Math. Soc. 36 (1972), 357–360. MR 308178, DOI 10.1090/S0002-9939-1972-0308178-8
- G. O. Michler and O. E. Villamayor, On rings whose simple modules are injective, J. Algebra 25 (1973), 185–201. MR 316505, DOI 10.1016/0021-8693(73)90088-4
- 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. II, Pacific J. Math. 39 (1971), 425–438. MR 306253, DOI 10.2140/pjm.1971.39.425
- Elmar Thoma, Über unitäre Darstellungen abzählbarer, diskreter Gruppen, Math. Ann. 153 (1964), 111–138 (German). MR 160118, DOI 10.1007/BF01361180
- Orlando E. Villamayor, On weak dimension of algebras, Pacific J. Math. 9 (1959), 941–951. MR 108527, DOI 10.2140/pjm.1959.9.941
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 194 (1974), 241-248
- MSC: Primary 16A26
- DOI: https://doi.org/10.1090/S0002-9947-1974-0357475-5
- MathSciNet review: 0357475