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Upper Bound of Multiplicity in Prime Characteristic by Huong, Duong Thi; Quy, Pham Hung is a scholarly article available to read on EtoBox.

What is Upper Bound of Multiplicity in Prime Characteristic about?

Let $(R, \frak m)$ be a local ring of prime characteristic $p$ of dimension $d$ with the embedding dimension $v$. Suppose the Frobenius test exponent for parameter ideals $Fte(R)$ of $R$ is finite, and let $Q = p^{Fte(R)}$. It is shown that $$e(R) \le Q^{v-d} \binom{v}{d}.$$ We also improve our bound for $F$-nilpotent rings. Our result extends the main results of Huneke and Watanabe and of Katzman and Zhang.

Author

Huong, Duong Thi; Quy, Pham Hung

Published

2019

Language

EN