Indecomposability of ideals in group rings
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- by M. M. Parmenter PDF
- Proc. Amer. Math. Soc. 91 (1984), 543 Request permission
Abstract:
Let $H$ be a subgroup of $G$ and let $I$ be the (two-sided) ideal of ${\mathbf {Z}}G$ generated by $\omega ({\mathbf {Z}}H)$. In this note, we show that $I$ is indecomposable as an ideal in ${\mathbf {Z}}G$. This extends a result of Linnell [1] and simplifies his argument somewhat.References
- P. A. Linnell, Indecomposability of the augmentation ideal as a two-sided ideal, J. Algebra 82 (1983), no. 2, 328–330. MR 704756, DOI 10.1016/0021-8693(83)90152-7
- 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
- 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
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 543
- MSC: Primary 16A26
- DOI: https://doi.org/10.1090/S0002-9939-1984-0746086-7
- MathSciNet review: 746086