Geodesic
On the radical of a group algebra over a commutative ring
Glasgow mathematical journal, Tome 18 (1977) no. 1, pp. 101-104

Voir la notice de l'article provenant de la source Cambridge University Press

Several people, including Wallace [4] and Passman [3], have studied the Jacobson radical of the group algebra F[G] where F is a field and G is a multiplicative group. In [4], for instance, Wallace proves that if G is an abelian group with Sylow p-subgroup P and if F is a field of characteristic p, then the Jacobson radical of F[G] equals the right ideal generated by the radical of F[P]. In this paper we shall study group algebras over arbitrary commutative rings. By a reduction to the case of a semi-simple commutative ring, we obtain Theorem 1 whose corollary contains a generalization of Wallace's theorem. Theorem 2, on the other hand, uses the first theorem to obtain results related to the main theorem of [3]. 
Potter, Gloria. On the radical of a group algebra over a commutative ring. Glasgow mathematical journal, Tome 18 (1977) no. 1, pp. 101-104. doi: 10.1017/S0017089500003104
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[1] 1.Connell, I. G., On the group ring, Canad. J. Math. 15 (1963), 650–685. Google Scholar | DOI

[2] 2.Passman, D. S., Infinite group rings (Marcel Dekker, 1971). Google Scholar

[3] 3.Passman, D. S., Radical ideals in group rings of locally finite groups, J. Algebra 33 (1975), 472–497. Google Scholar | DOI

[4] 4.Wallace, D. A. R., The Jacobson radicals of the group algebras of a group and of certain normal subgroups, Math. Z. 100 (1967), 282–294. Google Scholar | DOI

[5] 5.Woods, S. M., Some results on semi-perfect group rings, Canad. J. Math. 26 (1974), 121–129. Google Scholar | DOI

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