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並前往https://projecteuclid.org/journals/tokyo-journal-of-mathematics/volume-25/issue-2/Multiplicity-and-Hilbert-Kunz-Multiplicity-of-Monoid/10.3836/tjm/1244208851.pdf

Multiplicity and Hilbert-Kunz Multiplicity of Monoid Rings

binomial ideals I in a polynomial ring R over a field such that any monomial is a non zero divisor on R/I. Affine semigroup rings are monoid rings.

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