Upper bound of multiplicity in Cohen-Macaulay rings of prime characteristic

Abstract

Let (R,m) be a local ring of prime characteristic p and of dimension d with the embedding dimension v, type s and the Frobenius test exponent for parameter ideals Fte(R). We will give an upper bound for the multiplicity of Cohen-Macaulay rings in prime characteristic in terms of Fte(R), d, v and s. Our result extends the main results for Gorenstein rings due to Huneke and Watanabe