Let G be a discrete group, let
L2(G) denote the Hilbert space with Hilbert basis the elements of G, and let
W(G) denote the group von Neumann algebra of G. The class of elementary
amenable groups is the smallest class of groups which contains all abelian and all
finite groups, is extension closed, and is closed under directed unions. If
G is an elementary amenable group whose finite subgroups have bounded
order, α is a nonzero divisor in ℂG, and β is a nonzero element of L2(G),
we shall prove αβ≠0. We shall also consider the quotient rings of ℂG and
W(G).
