Linear systems and Multiplicity of ideals
نویسندگان
چکیده
A result of P. Samuel ([17] p. 186, Chap.II, Théorème 5) says that in a local noetherian ring (O,M) of Krull dimension d in which the residual field k is infinite, the multiplicity of a M-primary ideal I is equal to the multiplicity of an ideal (x1, . . . , xd) generated by some parameter sequence x1, . . . , xd contained in I. By a theorem of Rees ([16] p.142 Theorem 9.44), this implies that the ideals I and (x1, . . . , xd) have the same integral closure in the ring O.
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