Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
Fitting ideal; torsion submodule; regular element
Fitting ideal; torsion submodule; regular element
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.
References:
[1] Buchsbaum, D. A., Eisenbud, D.: What makes a complex exact?. J. Algebra 25 (1973), 259-268. DOI 10.1016/0021-8693(73)90044-6 | MR 0314819 | Zbl 0264.13007
[2] Eisenbud, D.: Commutative Algebra. With a View Toward Algebraic Geometry. Graduate Texts in Mathematics 150, Springer, New York (1995). DOI 10.1007/978-1-4612-5350-1 | MR 1322960 | Zbl 0819.13001
[3] Einsiedler, M., Ward, T.: Fitting ideals for finitely presented algebraic dynamical systems. Aequationes Math. 60 (2000), 57-71. DOI 10.1007/s000100050135 | MR 1777892 | Zbl 0972.22005
[4] Fitting, H.: Die Determinantenideale eines Moduls. Jahresber. Dtsch. Math.-Ver. 46 (1936), 195-228 German. Zbl 0016.05003
[5] Hadjirezaei, S., Hedayat, S.: On the first nonzero Fitting ideal of a module over a UFD. Commun. Algebra 41 (2013), 361-366. DOI 10.1080/00927872.2011.630851 | MR 3010542 | Zbl 1261.13004
[6] Hadjirezaei, S., Hedayat, S.: On finitely generated module whose first nonzero Fitting ideal is maximal. Commun. Algebra 46 (2018), 610-614. DOI 10.1080/00927872.2017.1324875 | MR 3764882 | Zbl 06875435
[7] Hadjirezaei, S., Karimzadeh, S.: On the first nonzero Fitting ideal of a module over a UFD II. Commun. Algebra 46 (2018), 5427-5432. DOI 10.1080/00927872.2018.1469027 | MR 3923770 | Zbl 1409.13019
[8] Huneke, C., Jorgensen, D. A., Katz, D.: Fitting ideals and finite projective dimension. Math. Proc. Camb. Philos. Soc. 138 (2005), 41-54. DOI 10.1017/S030500410400814X | MR 2127226 | Zbl 1099.13028
[9] Lipman, J.: On the Jacobian ideal of the module of differentials. Proc. Am. Math. Soc. 21 (1969), 422-426. DOI 10.1090/S0002-9939-1969-0237511-0 | MR 0237511 | Zbl 0174.52703
[10] Lu, C.-P.: Prime submodules of modules. Comment. Math. Univ. St. Pauli 33 (1984), 61-69. MR 0741378 | Zbl 0575.13005
[11] Northcott, D. G.: Finite Free Resolutions. Cambridge Tracts in Mathematics 71, Cambridge University Press, Cambridge (1976). DOI 10.1017/CBO9780511565892 | MR 0460383 | Zbl 0328.13010
Search
Partner of
