Upper Bound of Multiplicity in Cohen-Macaulay Rings of Prime Characteristic
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 [8].