  A finitely generated module C over a commutative noetherian ring R is
semidualizing if Hom_R(C,C) \cong R and Ext^i_R(C,C) = 0 for all i \geq 1. For
certain local Cohen-Macaulay rings (R,m), we verify the equality of
Hilbert-Samuel multiplicities e_R(J;C) = e_R(J;R) for all semidualizing
R-modules C and all m-primary ideals J. The classes of rings we investigate
include those that are determined by ideals defining fat point schemes in
projective space or by monomial ideals.
