ARTINIAN-FINITARY GROUPS OVER COMMUTATIVE RINGS AND NON-COMMUTATIVE RINGS

摘要

Let M be a module over the ring R. Extensive use is made of Krull codimension to study further the Artinian-finitary automorphism group F_1Aut_RM = {g ∈ Aut_R M: M (g-1) is R-Artinian} of M over R. Substantial progress is made where either M is residually Noetherian or R is commutative. There are some group-theoretic consequences of the two main structure theorems.