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 AnnkA(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.