On a change of rings for mixed multiplicities
Bull. Korean Math. Soc. 2020 Vol. 57, No. 5, 1251-1258
Published online September 30, 2020
Truong Thi Hong Thanh, Duong Quoc Viet
Hanoi National University of Education; 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
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