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Ideals and their Fitting ideals

Part of: Algebraic combinatorics Theory of modules and ideals

Published online by Cambridge University Press:  30 July 2025

DAVID EISENBUD ,
ANTONINO FICARRA ,
JÜRGEN HERZOG  and
SOMAYEH MORADI
DAVID EISENBUD
Affiliation:
Department of Mathematics, University of California at Berkeley, and the Mathematical Science Research Institute, Berkeley, CA, 94720, U.S.A. e-mail: de@msri.org
ANTONINO FICARRA
Affiliation:
Department of Mathematics and Computer Sciences, Physics and Earth Sciences, University of Messina, Viale Ferdinando Stagno d’Alcontres 31, 98166 Messina, Italy. e-mail: antficarra@unime.it
JÜRGEN HERZOG
Affiliation:
Fakultät für Mathematik, Universität Duisburg-Essen, 45117 Essen, Germany. e-mail: juergen.herzog@uni-essen.de
SOMAYEH MORADI
Affiliation:
Department of Mathematics, Faculty of Science, Ilam University, P.O.Box 69315-516, Ilam, Iran. e-mail: so.moradi@ilam.ac.ir
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Abstract

For an ideal I in a Noetherian ring R, the Fitting ideals $\mathrm{Fitt}_j(I)$ are studied. We discuss the question of when $\mathrm{Fitt}_j(I)=I$ or $\sqrt{\mathrm{Fitt}_j(I)}=\sqrt{I}$ for some j. A classical case is the Hilbert–Burch theorem when $j=1$ and I is a perfect ideal of grade 2 in a local ring.

MSC classification

Primary: 13C05: Structure, classification theorems
Secondary: 05E40: Combinatorial aspects of commutative algebra

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , First View , pp. 1 - 13
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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