A property of finite $p$-groups
HTML articles powered by AMS MathViewer
- by Shoichi Kondo PDF
- Proc. Amer. Math. Soc. 67 (1977), 35-37 Request permission
Abstract:
Let $R(G)$ denote the character ring of a finite group G and let $\Lambda$ be a commutative ring with identity. In this paper we show that if $G \ne \{ 1\}$, then $\Lambda { \otimes _Z}R(G)$ has only one maximal ideal if and only if G is a p-group and $\Lambda$ has only one maximal ideal m such that $\Lambda /\mathfrak {m}$ is of characteristic p.References
- Paul J. Allen and Joseph Neggers, A characterization of Steinitz group rings, Proc. Amer. Math. Soc. 49 (1975), 39–42. MR 360668, DOI 10.1090/S0002-9939-1975-0360668-0
- M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0242802
- Byoung-song Chwe and Joseph Neggers, On the extension of linearly independent subsets of free modules to bases, Proc. Amer. Math. Soc. 24 (1970), 466–470. MR 252432, DOI 10.1090/S0002-9939-1970-0252432-3
- B. S. Chwe and J. Neggers, Local rings with left vanishing radical, J. London Math. Soc. (2) 4 (1971), 374–378. MR 289558, DOI 10.1112/jlms/s2-4.2.374
- Tor Gulliksen, Paulo Ribenboim, and T. M. Viswanathan, An elementary note on group-rings, J. Reine Angew. Math. 242 (1970), 148–162. MR 274609, DOI 10.1515/crll.1970.242.148
- Jean-Pierre Serre, Représentations linéaires des groupes finis, Hermann, Paris, 1971 (French). Deuxième édition, refondue. MR 0352231
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 67 (1977), 35-37
- MSC: Primary 20C15
- DOI: https://doi.org/10.1090/S0002-9939-1977-0460439-2
- MathSciNet review: 0460439