Title: Hilbert-kunz multiplicity, PhanTom projective dimension by specialization Authors: Dam, Van Nhi Keywords: Hilbert-kunz multiplicity;PhanTom projective dimension Issue Date: 2002 Publisher: H. : ĐHQGHN Series/Report no.: Vol. 18;No. 4 (2002) URI: http://repository.vnu.edu.vn/handle/VNU_123/58414 The ground field k is assumed to be infinite. Wo denote by K a field extension of k Let X = ( x ir ..,x n) be indeterminates. Let u = ( t i l , u m) be a family of indeterminates, which arc considered as parameters. The specialization of an ideal / of H = fc(u)(x] with respect to the substitution u —y o. = (a i, ...am) 6 K rn was defined as the ideal Ja , which is generated by the set {/( a , x ) \ f ( u , x ) € I u fc[u,x]}. The theory of specialization of ideals was introduced by w . Krull. Krull has showed that the ideal / a inherits most of basic properties if I and it was used to prove many important results in algebra and in algebr...
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