منابع مشابه
Good Ideals in Gorenstein Local Rings
Let I be an m-primary ideal in a Gorenstein local ring (A,m) with dimA = d, and assume that I contains a parameter ideal Q in A as a reduction. We say that I is a good ideal in A if G = ∑ n≥0 I n/In+1 is a Gorenstein ring with a(G) = 1−d. The associated graded ring G of I is a Gorenstein ring with a(G) = −d if and only if I = Q. Hence good ideals in our sense are good ones next to the parameter...
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...
متن کاملComplete Ideals in 2-dimensional Regular Local Rings
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. Zarisk...
متن کاملMultiplier Ideals in Two-dimensional Local Rings with Rational Singularities
The aim of this paper is to study jumping numbers and multiplier ideals of any ideal in a two-dimensional local ring with a rational singularity. In particular we reveal which information encoded in a multiplier ideal determines the next jumping number. This leads to an algorithm to compute sequentially the jumping numbers and the whole chain of multiplier ideals in any desired range. As a cons...
متن کاملIdeals in Computable Rings
We show that the existence of a nontrivial proper ideal in a commutative ring with identity which is not a eld is equivalent to WKL0 over RCA0, and that the existence of a nontrivial proper nitely generated ideal in a commutative ring with identity which is not a eld is equivalent to ACA0 over RCA0. We also prove that there are computable commutative rings with identity where the nilradical is ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2002
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.9099