``Augmentation ideals of equivariant cohomology rings.''
J.P.C.Greenlees 

School of Mathematics and Statistics, 
Hicks Building, 
Sheffield S3 7RH. 
UK.


The purpose of this note is to establish a number of useful results about
the augmentation ideal $J$ for the coefficient ring $F_G^*$
of a Noetherian complex orientable  equivariant cohomology 
theory. The results show that various naturally occurring substitutes
for the ideal have the same radical, and can therefore be used instead of the 
augmentation ideal in all geometric constructions.