Geodesic
Decomposition of finitely generated modules using Fitting ideals
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 1179-1190
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/CMJ.2020.0350-19
Classification : 13C05, 13D05
Keywords: Fitting ideal; torsion submodule; regular element 
@article{10_21136_CMJ_2020_0350_19,
     author = {Hadjirezaei, Somayeh and Hedayat, Sina},
     title = {Decomposition of finitely generated modules using {Fitting} ideals},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1179--1190},
     year = {2020},
     volume = {70},
     number = {4},
     doi = {10.21136/CMJ.2020.0350-19},
     mrnumber = {4181806},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0350-19/}
}
TY  - JOUR
AU  - Hadjirezaei, Somayeh
AU  - Hedayat, Sina
TI  - Decomposition of finitely generated modules using Fitting ideals
JO  - Czechoslovak Mathematical Journal
PY  - 2020
SP  - 1179
EP  - 1190
VL  - 70
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0350-19/
DO  - 10.21136/CMJ.2020.0350-19
LA  - en
ID  - 10_21136_CMJ_2020_0350_19
ER  - 
%0 Journal Article
%A Hadjirezaei, Somayeh
%A Hedayat, Sina
%T Decomposition of finitely generated modules using Fitting ideals
%J Czechoslovak Mathematical Journal
%D 2020
%P 1179-1190
%V 70
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0350-19/
%R 10.21136/CMJ.2020.0350-19
%G en
%F 10_21136_CMJ_2020_0350_19
Hadjirezaei, Somayeh; Hedayat, Sina. Decomposition of finitely generated modules using Fitting ideals. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 1179-1190. doi: 10.21136/CMJ.2020.0350-19

[1] Buchsbaum, D. A., Eisenbud, D.: What makes a complex exact?. J. Algebra 25 (1973), 259-268. | DOI | MR | JFM

[2] Eisenbud, D.: Commutative Algebra. With a View Toward Algebraic Geometry. Graduate Texts in Mathematics 150, Springer, New York (1995). | DOI | MR | JFM

[3] Einsiedler, M., Ward, T.: Fitting ideals for finitely presented algebraic dynamical systems. Aequationes Math. 60 (2000), 57-71. | DOI | MR | JFM

[4] Fitting, H.: Die Determinantenideale eines Moduls. Jahresber. Dtsch. Math.-Ver. 46 (1936), 195-228 German. | JFM

[5] Hadjirezaei, S., Hedayat, S.: On the first nonzero Fitting ideal of a module over a UFD. Commun. Algebra 41 (2013), 361-366. | DOI | MR | JFM

[6] Hadjirezaei, S., Hedayat, S.: On finitely generated module whose first nonzero Fitting ideal is maximal. Commun. Algebra 46 (2018), 610-614. | DOI | MR | JFM

[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 | MR | JFM

[8] Huneke, C., Jorgensen, D. A., Katz, D.: Fitting ideals and finite projective dimension. Math. Proc. Camb. Philos. Soc. 138 (2005), 41-54. | DOI | MR | JFM

[9] Lipman, J.: On the Jacobian ideal of the module of differentials. Proc. Am. Math. Soc. 21 (1969), 422-426. | DOI | MR | JFM

[10] Lu, C.-P.: Prime submodules of modules. Comment. Math. Univ. St. Pauli 33 (1984), 61-69. | MR | JFM

[11] Northcott, D. G.: Finite Free Resolutions. Cambridge Tracts in Mathematics 71, Cambridge University Press, Cambridge (1976). | DOI | MR | JFM

Cité par Sources :