×

Decomposition of finitely generated modules using Fitting ideals. (English) Zbl 07285989

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.

MSC:

13C05 Structure, classification theorems for modules and ideals in commutative rings
13D05 Homological dimension and commutative rings
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Buchsbaum, D. A.; Eisenbud, D., What makes a complex exact?, J. Algebra 25 (1973), 259-268
[2] Eisenbud, D., Commutative Algebra. With a View Toward Algebraic Geometry, Graduate Texts in Mathematics 150, Springer, New York (1995)
[3] Einsiedler, M.; Ward, T., Fitting ideals for finitely presented algebraic dynamical systems, Aequationes Math. 60 (2000), 57-71
[4] Fitting, H., Die Determinantenideale eines Moduls, Jahresber. Dtsch. Math.-Ver. 46 (1936), 195-228 German
[5] Hadjirezaei, S.; Hedayat, S., On the first nonzero Fitting ideal of a module over a UFD, Commun. Algebra 41 (2013), 361-366
[6] Hadjirezaei, S.; Hedayat, S., On finitely generated module whose first nonzero Fitting ideal is maximal, Commun. Algebra 46 (2018), 610-614
[7] Hadjirezaei, S.; Karimzadeh, S., On the first nonzero Fitting ideal of a module over a UFD II, Commun. Algebra 46 (2018), 5427-5432
[8] Huneke, C.; Jorgensen, D. A.; Katz, D., Fitting ideals and finite projective dimension, Math. Proc. Camb. Philos. Soc. 138 (2005), 41-54
[9] Lipman, J., On the Jacobian ideal of the module of differentials, Proc. Am. Math. Soc. 21 (1969), 422-426
[10] Lu, C.-P., Prime submodules of modules, Comment. Math. Univ. St. Pauli 33 (1984), 61-69
[11] Northcott, D. G., Finite Free Resolutions, Cambridge Tracts in Mathematics 71, Cambridge University Press, Cambridge (1976)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.