Complete Ideals in 2-dimensional Regular Local Rings
نویسنده
چکیده
The objective of these notes is to present a few important results about complete ideals in 2–dimensional regular local rings. The fundamental theorems about such ideals are due to Zariski found in appendix 5 of [26]. These results were proved by Zariski in [27] for 2dimensional polynomial rings over an algebraically closed field of characteristic zero and rings of holomorphic functions. Zariski states in [27],
منابع مشابه
ON FINITENESS OF PRIME IDEALS IN NORMED RINGS
In a commutative Noetherian local complex normed algebra which is complete in its M-adic metric there are only finitely many closed prime ideals.
متن کاملIntegrally Closed Ideals in Two-dimensional Regular Local Rings Are Multiplier Ideals
Multiplier ideals in commutative rings are certain integrally closed ideals with properties that lend themselves to highly interesting applications. How special are they among integrally closed ideals in general? We show that in a two-dimensional regular local ring with algebraically closed residue field there is in fact no difference between “multiplier” and “integrally closed” (or “complete.”...
متن کاملIntegrally Closed Finite-colength Ideals in Two-dimensional Regular Local Rings Are Multiplier Ideals
Introduction. There has arisen in recent years a substantial body of work on “multiplier ideals” in commutative rings (see [La]). Multiplier ideals are integrally closed ideals with properties that lend themselves to highly interesting applications. One is tempted then to ask just how special multiplier ideals are among integrally closed ideals in general. In this note we show that in a two-dim...
متن کاملec 1 99 3 Complete ideals defined by sign conditions and the real spectrum of a two - dimensional local ring
0. Introduction. Let (A,m) be a regular local ring and let α and β be points of the real spectrum of A centered at m . α and β may be viewed as total orderings on quotients of A . Associated with α and β , there is the so-called “separating ideal”, 〈α, β〉 ⊆ A , which is generated by all a ∈ A such that a is non-negative with respect to α and −a is non-negative with respect to β . 〈α, β〉 is a va...
متن کاملAdjoint ideals and Gorenstein blowups in two-dimensional regular local rings
In this article we investigate when a complete ideal in a twodimensional regular local ring is a multiplier ideal of some ideal with an integral multiplying parameter. In particular, we show that this question is closely connected to the Gorenstein property of the blowup along the ideal.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012