On the projectivity of finitely generated flat modules

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A. Tarizadeh

Abstract

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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How to Cite
Tarizadeh, A. (2020). On the projectivity of finitely generated flat modules. Extracta Mathematicae, 35(1), 55-67. Retrieved from https://publicaciones.unex.es/index.php/EM/article/view/2605-5686.35.1.55
Section
Commutative Algebra

References

[1] N. Bourbaki, “Algèbre Commutative”, Chapitres 1 à 4, Springer, Berlin, 2006.
[2] H. Cartan, S. Eilenberg, “Homological Algebra”, Princeton University Press, Princeton, N. J., 1956.
[3] S.H. Cox Jr., R.L. Pendleton, Rings for which certain flat modules are projective, Trans. Amer. Math. Soc. 150 (1970), 139 – 156.
[4] A.J. de Jong et al., Stacks Project. http://stacks.math.columbia.edu
[5] S. Endo, On flat modules over commutative rings, J. Math. Soc. Japan 14 (3) (1962), 284 – 291.
[6] A. Facchini et al., Finitely generated flat modules and a characterization of semiperfect rings, Comm. Algebra 31 (9) (2003), 4195 – 4214.
[7] S. Jondrup, On finitely generated flat modules, Math. Scand. 26 (1970), 233 – 240.
[8] I. Kaplansky, Projective modules, Ann. of Math. 68 (1958), 372 – 377.
[9] H. Matsumura, “Commutative Ring Theory”, Cambridge University Press, Cambridge, 1989.
[10] J.P. Olivier, Anneaux absolument plats universels et épimorphismes à buts réduits, in “Séminaire Samuel. Algèbre Commutative”, Tomme 2 (6) (1967- 1968), 1 – 12.
[11] G. Puninski, P. Rothmaler, When every finitely generated flat module is projective, J. Algebra 277 (2004), 542 – 558.
[12] W. Vasconcelos, On finitely generated flat modules, Trans. Amer. Math. Soc. 138 (1969), 505 – 512.
[13] R. Wiegand, Globalization theorems for locally finitely generated modules, Pacific J. Math. 39 (1) (1971), 269 – 274.