Bulletin of the
Korean Mathematical Society BKMS

This paper establishes a formula changing the ring from a Noetherian local ring $A$ of dimension $d > 0$ containing the residue field $k$ to the polynomial ring in $d$ variables $k[X_1, X_2,\ldots, X_d]$ for mixed multiplicities. And as consequences, we get a formula for the multiplicity of Rees rings and formulas for mixed multiplicities and the multiplicity of Rees rings of quotient rings of $A$ by highest dimensional associated prime ideals of $A$.

Keywords: Mixed multiplicity, Hilbert-Samuel multiplicity, Noetherian ring

MSC numbers: Primary 13H15; Secondary 13C15, 13D40