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Kernel Coefficient Ideals in Noetherian Rings

Authors
Journal
Journal of Algebra
0021-8693
Publisher
Elsevier
Publication Date
Volume
179
Issue
3
Identifiers
DOI: 10.1006/jabr.1996.0030

Abstract

Abstract A new ideal I*, the kernel coefficient ideal of a nonprincipal ideal I, is introduced in a commutative Noetherian ring R. Various properties of this ideal and its relations with many other standard concepts are studied. I* is also examined in terms of a sequence of subideals I n and the relation type of Iwhen Ris a local ring. Several characterizations of I* are given in terms of the kernels of certain ring homomorphisms, and then it is shown that this new ideal has many nice applications, especially in the study of asymptotic prime divisors.

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