Decomposition of finitely generated modules using Fitting ideals

Somayeh Hadjirezaei; Sina Hedayat

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 4, page 1179-1190
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Hadjirezaei, Somayeh, and Hedayat, Sina. "Decomposition of finitely generated modules using Fitting ideals." Czechoslovak Mathematical Journal 70.4 (2020): 1179-1190. <http://eudml.org/doc/297348>.

@article{Hadjirezaei2020,
abstract = {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.},
author = {Hadjirezaei, Somayeh, Hedayat, Sina},
journal = {Czechoslovak Mathematical Journal},
keywords = {Fitting ideal; torsion submodule; regular element},
language = {eng},
number = {4},
pages = {1179-1190},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Decomposition of finitely generated modules using Fitting ideals},
url = {http://eudml.org/doc/297348},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Hadjirezaei, Somayeh
AU - Hedayat, Sina
TI - Decomposition of finitely generated modules using Fitting ideals
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 4
SP - 1179
EP - 1190
AB - 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.
LA - eng
KW - Fitting ideal; torsion submodule; regular element
UR - http://eudml.org/doc/297348
ER -

References

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  1. Buchsbaum, D. A., Eisenbud, D., 10.1016/0021-8693(73)90044-6, J. Algebra 25 (1973), 259-268. (1973) Zbl0264.13007MR0314819DOI10.1016/0021-8693(73)90044-6
  2. Eisenbud, D., 10.1007/978-1-4612-5350-1, Graduate Texts in Mathematics 150, Springer, New York (1995). (1995) Zbl0819.13001MR1322960DOI10.1007/978-1-4612-5350-1
  3. Einsiedler, M., Ward, T., 10.1007/s000100050135, Aequationes Math. 60 (2000), 57-71. (2000) Zbl0972.22005MR1777892DOI10.1007/s000100050135
  4. Fitting, H., Die Determinantenideale eines Moduls, Jahresber. Dtsch. Math.-Ver. 46 (1936), 195-228 German. (1936) Zbl0016.05003
  5. Hadjirezaei, S., Hedayat, S., 10.1080/00927872.2011.630851, Commun. Algebra 41 (2013), 361-366. (2013) Zbl1261.13004MR3010542DOI10.1080/00927872.2011.630851
  6. Hadjirezaei, S., Hedayat, S., 10.1080/00927872.2017.1324875, Commun. Algebra 46 (2018), 610-614. (2018) Zbl06875435MR3764882DOI10.1080/00927872.2017.1324875
  7. Hadjirezaei, S., Karimzadeh, S., 10.1080/00927872.2018.1469027, Commun. Algebra 46 (2018), 5427-5432. (2018) Zbl1409.13019MR3923770DOI10.1080/00927872.2018.1469027
  8. Huneke, C., Jorgensen, D. A., Katz, D., 10.1017/S030500410400814X, Math. Proc. Camb. Philos. Soc. 138 (2005), 41-54. (2005) Zbl1099.13028MR2127226DOI10.1017/S030500410400814X
  9. Lipman, J., 10.1090/S0002-9939-1969-0237511-0, Proc. Am. Math. Soc. 21 (1969), 422-426. (1969) Zbl0174.52703MR0237511DOI10.1090/S0002-9939-1969-0237511-0
  10. Lu, C.-P., Prime submodules of modules, Comment. Math. Univ. St. Pauli 33 (1984), 61-69. (1984) Zbl0575.13005MR0741378
  11. Northcott, D. G., 10.1017/CBO9780511565892, Cambridge Tracts in Mathematics 71, Cambridge University Press, Cambridge (1976). (1976) Zbl0328.13010MR0460383DOI10.1017/CBO9780511565892

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