On commutative invariants for modules over crossed products of minimax nilpotent linear groups

Let N be a minimax nilpotent torsion-free normal subgroup of a soluble group G of finite rank, R be a finitely generated commutative domain and R*N be a crossed product of R and N. In the paper we construct a correspondence between an R*N-module W and a finite set M of equivalent classes of prime ideals minimal over Ann₊₀ (W/WI), where kA is a group algebra of an abelian minimax group A and I is an appropriative G-invariant ideal of RG. It is shown that if Wg W for all g g then the action of the group G by conjugations on N can be extended to an action of the group G on the set M. The results allow us to apply methods of commutative algebra to the study of W.