Про обмежено артiновi фiнiтарнi модулi

Abstract

We consider a following special case of Artinian finitary modules. Let D be a Dedekind domain and G is a group. The DG-module A is said to be bounded Artinian finitary, if A is Artinian finitary, and there are the numbers bF (A) = b, bd(A) = d, b, d ∈ N and a finite subset bσ(A) = τ ⊆ Spec(D) such that lF (A/CA(g)) 6 b, ld(A/CA(g)) 6 d and AssD(A/CA(g)) ⊆ τ for every element g ∈ G. Here, we study the bounded Artinian finitary modules under some natural restriction.