Big tight closure test elements for some non-reduced excellent rings
نویسندگان
چکیده
منابع مشابه
Relative test elements for tight closure
Test ideals play a crucial role in the theory of tight closure developed by Melvin Hochster and Craig Huneke. Recently, Karen Smith showed that test ideals are closely related to certain multiplier ideals that arise in vanishing theorems in algebraic geometry. In this paper we develop a generalization of the notion of test ideals: for complete local rings R and S, where S is a module-6nite exte...
متن کاملTight Closure in Non–equidimensional Rings
Throughout our discussion, all rings are commutative, Noetherian and have an identity element. The notion of the tight closure of an ideal was developed by M. Hochster and C. Huneke in [HH1] and has yielded many elegant and powerful results in commutative algebra. The theory leads to the notion of F–rational rings, defined by R. Fedder and K.-i. Watanabe as rings in which parameter ideals are t...
متن کاملTight Closure in Graded Rings
This paper facilitates the computation of tight closure by giving giving upper and lower bounds on the degrees of elements that need to be checked for inclusion in the tight closure of certain homogeneous ideals in a graded ring. Differential operators are introduced to the study of tight closure, and used to prove that the degree of any element in the tight closure of a homogeneous ideal (but ...
متن کاملLocalization and Test Exponents for Tight Closure
We introduce the notion of a test exponent for tight closure, and explore its relationship with the problem of showing that tight closure commutes with localization, a longstanding open question. Roughly speaking, test exponents exist if and only if tight closure commutes with localization: mild conditions on the ring are needed to prove this. We give other, independent, conditions that are nec...
متن کاملIntegral Closure of Ideals in Excellent Local Rings
In [1] Briançon and Skoda proved, using analytic methods, that if I is an ideal in the convergent power series ring C{x1, . . . , xn} then In, the integral closure of I, is contained in I. Extensive work has been done in the direction of proving “Briançon-Skoda type theorems”, that is, statements about I t being contained in (I t−k)#, where k is a constant independent of t, and # is a closure o...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2012
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2011.08.009