On the projectivity of finitely generated flat modules

Autores/as

  • A: Tarizadeh Department of Mathematics, Faculty of Basic Sciences, University of Maragheh P.O. Box 55136–553, Maragheh, Iran

DOI:

https://doi.org/10.17398/2605-5686.35.1.55

Palabras clave:

exterior power, invariant factor, projectivity, S-ring, specialization cone, generalization cone

Resumen

In this paper, the projectivity of a finitely generated flat module of a commutative ring is studied through its exterior powers and invariant factors and then various new results are obtained. Specially, the related results of Endo, Vasconcelos, Wiegand, Cox-Rush and Puninski-Rothmaler on the projectivity of finitely generated flat modules are generalized.

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Referencias

N. Bourbaki, “Algèbre Commutative”, Chapitres 1 à 4, Springer, Berlin, 2006.

H. Cartan, S. Eilenberg, “Homological Algebra”, Princeton University Press, Princeton, N. J., 1956.

S.H. Cox Jr., R.L. Pendleton, Rings for which certain flat modules are projective, Trans. Amer. Math. Soc. 150 (1970), 139 – 156.

A.J. de Jong et al., Stacks Project. http://stacks.math.columbia.edu

S. Endo, On flat modules over commutative rings, J. Math. Soc. Japan 14 (3) (1962), 284 – 291.

A. Facchini et al., Finitely generated flat modules and a characterization of semiperfect rings, Comm. Algebra 31 (9) (2003), 4195 – 4214.

S. Jondrup, On finitely generated flat modules, Math. Scand. 26 (1970), 233 – 240.

I. Kaplansky, Projective modules, Ann. of Math. 68 (1958), 372 – 377.

H. Matsumura, “Commutative Ring Theory”, Cambridge University Press, Cambridge, 1989.

J.P. Olivier, Anneaux absolument plats universels et épimorphismes à buts réduits, in “Séminaire Samuel. Algèbre Commutative”, Tomme 2 (6) (1967- 1968), 1 – 12.

G. Puninski, P. Rothmaler, When every finitely generated flat module is projective, J. Algebra 277 (2004), 542 – 558.

W. Vasconcelos, On finitely generated flat modules, Trans. Amer. Math. Soc. 138 (1969), 505 – 512.

R. Wiegand, Globalization theorems for locally finitely generated modules, Pacific J. Math. 39 (1) (1971), 269 – 274.

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Publicado

2020-06-01

Número

Sección

Commutative Algebra

Cómo citar

On the projectivity of finitely generated flat modules. (2020). Extracta Mathematicae, 35(1), 55-67. https://doi.org/10.17398/2605-5686.35.1.55