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Clôture intégrale des idéaux et équisingularité

Monique Lejeune-Jalabert, Bernard Teissier (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

This text has two parts. The first one is the essentially unmodified text of our 1973-74 seminar on integral dependence in complex analytic geometry at the Ecole Polytechnique with J-J. Risler’s appendix on the Łojasiewicz exponents in the real-analytic framework. The second part is a short survey of more recent results directly related to the content of the seminar.The first part begins with the definition and elementary properties of the ν ¯ order function associated to an ideal I of a reduced analytic...

C(X) vs. C(X) modulo its socle

F. Azarpanah, O. A. S. Karamzadeh, S. Rahmati (2008)

Colloquium Mathematicae

Let C F ( X ) be the socle of C(X). It is shown that each prime ideal in C ( X ) / C F ( X ) is essential. For each h ∈ C(X), we prove that every prime ideal (resp. z-ideal) of C(X)/(h) is essential if and only if the set Z(h) of zeros of h contains no isolated points (resp. int Z(h) = ∅). It is proved that d i m ( C ( X ) / C F ( X ) ) d i m C ( X ) , where dim C(X) denotes the Goldie dimension of C(X), and the inequality may be strict. We also give an algebraic characterization of compact spaces with at most a countable number of nonisolated points. For each essential...

Fiber cones and the integral closure of ideals.

R. Hübl, C. Huneke (2001)

Collectanea Mathematica

Let (R,m) be a Noetherian local ring and let I C R be an ideal. This paper studies the question of when m I is integrally closed. Particular attention is focused on the case R is a regular local ring and I is a reduced ideal. This question arose through a question posed by Eisenbud and Mazur on the existence of evolutions.

Integral closures of ideals in the Rees ring

Y. Tiraş (1993)

Colloquium Mathematicae

The important ideas of reduction and integral closure of an ideal in a commutative Noetherian ring A (with identity) were introduced by Northcott and Rees [4]; a brief and direct approach to their theory is given in [6, (1.1)]. We begin by briefly summarizing some of the main aspects.

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