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 On a Change of Rings for Mixed Multiplicities Bull. Korean Math. Soc.Published online June 29, 2020 Truong Thi Hong Thanh and Duong Quoc Viet Hanoi National University of Education Abstract : 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, 14C17. Full-Text :