Geodesic
Modules over polycyclic groups have many irreducible images
Glasgow mathematical journal, Tome 22 (1981) no. 2, pp. 141-150

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

Recall that a Noetherian ring R is a Hilbert ring if the Jacobson radical of every factor ring of R is nilpotent. As one of the main results of [13], J. E. Roseblade proved that if J is a commutative Hilbert ring and G is a polycyclic-by-finite group then JG is a Hilbert ring. The main theorem of this paper is a generalisation of this result in the case where all the field images of J are absolute fields—we shall say that J is absolutely Hilbert. The result is stated in terms of the (Gabriel–Rentschler–) Krull dimension; the definition and basic properties of this may be found in [5]. Let M be a finitely generated right module over the ring R. We write AnnR(M) (or just Ann(M)) for the ideal {r ∈ R: Mr = 0}, the annihilator of M in R. If M is also a left module, its left annihilator will be denoted l-AnnR(M). If R is a group ring JG, put 
Brown, Kenneth A. Modules over polycyclic groups have many irreducible images. Glasgow mathematical journal, Tome 22 (1981) no. 2, pp. 141-150. doi: 10.1017/S0017089500004584
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