THE F-DECOMPOSITION OF ARTINIAN-MODULES OVER HYPERFINITE GROUPS

A ZG-module A is said to have an f-decomposition if A=A(f) circle plus A(($) over bar f) in which A(f) is a EG-submodule of A such that each irreducible ZG-factor of A(f) as an abelian group is finite and the HG-submodule A(($) over bar f) has no finite irreducible ZG-Factors. Tn this paper, we prove that: if G is a hyperfinite group then any artinian ZG-module A has an f-decomposition, which gives a positive answer to the question raised by D.I. Zaitzev in 1986.