Let k be the ground field k and X = (xo,... , x n ) be indeterminates. Let I be a graded ideal of k[x]. In [2], [3] there are formulas to determine the Betti numbers and multiplicity of R / I . Now we want to give an extension and a new simple proof about a result of Huneke and Miller and we also consider the algebra with minimal multiplicity.
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Let k be the ground field k and X = (xo,... , x n ) be indeterminates. Let I be a graded ideal of k[x]. In [2], [3] there are formulas to determine the Betti numbers and multiplicity of R / I . Now we want to give an extension and a new simple proof about a result of Huneke and Miller and we also consider the algebra with minimal multiplicity.