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Title: Decomposition of finitely generated modules using Fitting ideals (English)
Author: Hadjirezaei, Somayeh
Author: Hedayat, Sina
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 70
Issue: 4
Year: 2020
Pages: 1179-1190
Summary lang: English
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Category: math
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Summary: Let $R$ be a commutative Noetherian ring and $M$ be a finitely generated $R$-module. The main result of this paper is to characterize modules whose first nonzero Fitting ideal is a product of maximal ideals of $R$, in some cases. (English)
Keyword: Fitting ideal
Keyword: torsion submodule
Keyword: regular element
MSC: 13C05
MSC: 13D05
idZBL: 07285989
idMR: MR4181806
DOI: 10.21136/CMJ.2020.0350-19
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Date available: 2020-11-18T09:50:54Z
Last updated: 2023-01-02
Stable URL: http://hdl.handle.net/10338.dmlcz/148421
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Reference: [5] Hadjirezaei, S., Hedayat, S.: On the first nonzero Fitting ideal of a module over a UFD.Commun. Algebra 41 (2013), 361-366. Zbl 1261.13004, MR 3010542, 10.1080/00927872.2011.630851
Reference: [6] Hadjirezaei, S., Hedayat, S.: On finitely generated module whose first nonzero Fitting ideal is maximal.Commun. Algebra 46 (2018), 610-614. Zbl 06875435, MR 3764882, 10.1080/00927872.2017.1324875
Reference: [7] Hadjirezaei, S., Karimzadeh, S.: On the first nonzero Fitting ideal of a module over a UFD II.Commun. Algebra 46 (2018), 5427-5432. Zbl 1409.13019, MR 3923770, 10.1080/00927872.2018.1469027
Reference: [8] Huneke, C., Jorgensen, D. A., Katz, D.: Fitting ideals and finite projective dimension.Math. Proc. Camb. Philos. Soc. 138 (2005), 41-54. Zbl 1099.13028, MR 2127226, 10.1017/S030500410400814X
Reference: [9] Lipman, J.: On the Jacobian ideal of the module of differentials.Proc. Am. Math. Soc. 21 (1969), 422-426. Zbl 0174.52703, MR 0237511, 10.1090/S0002-9939-1969-0237511-0
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