HILBERT FUNCTION AND MULTIPLICITYOF IDEALIZTIONS

Abstract

Let (
R,
m
) be a Noetherian local ring and
M
a finitely generated
R
-
module. We study the relations of the Hilbert function, the multiplicity
of an
m
-primary ideal of
R
and these of
m
×
M
-primary ideal of the ide-
alization. Some applications to the Cohen-Macaulayness of idealization
are given