Rocky Mountain Journal of Mathematics

On torsion free and cotorsion discrete modules

Edgar Enochs, J.R. García Rozas, Luis Oyonarte, and Blas Torrecillas

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We prove that, if $\mathcal F $ is the class of torsion free discrete modules over a profinite group $G$, that is, the class of discrete $G$-modules which are torsion free as abelian groups, then $({\mathcal F},{\mathcal F}^\bot )$ is a complete cotorsion pair. Moreover, we find a structure theorem for torsion free and cotorsion discrete $G$-modules and for finitely generated cotorsion discrete $G$-modules.

Article information

Rocky Mountain J. Math., Volume 47, Number 2 (2017), 429-444.

First available in Project Euclid: 18 April 2017

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Zentralblatt MATH identifier

Primary: 18G25: Relative homological algebra, projective classes

Torsion free discrete module cotorsion module


Enochs, Edgar; Rozas, J.R. García; Oyonarte, Luis; Torrecillas, Blas. On torsion free and cotorsion discrete modules. Rocky Mountain J. Math. 47 (2017), no. 2, 429--444. doi:10.1216/RMJ-2017-47-2-429.

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  • E. Enochs, Torsion free covering modules, Proc. Amer. Math. Soc. 14 (1963), 884–890.
  • E. Enochs, S. Estrada and B. Torrecillas, Gorenstein flat covers and Gorenstein cotorsion modules over integral group rings, Alg. Rep. Theory 8 (2005), 525–539.
  • E. Enochs, J.R. García Rozas and L. Oyonarte, Finitely generated cotorsion modules, Proc. Edinburgh Math. Soc. 44 (2001), 43–152.
  • E. Enochs, J.R. García Rozas, L. Oyonarte and B. Torrecillas, On Gorenstein injective discrete modules over profinite groups, Acta Math. Hung. 142 (2014), 296–316.
  • E. Enochs and O. Jenda, Relative homological algebra, de Gruyter Expos. Math. 30, Walter de Gruyter, Berlin, 2000.
  • E. Enochs and E. Khan, Flat discrete modules over profinite groups, Comm. Algebra 42 (2014), 2331–2337.
  • E. Enochs and L. Oyonarte, Flat covers and cotorsion envelopes of sheaves, Proc. Amer. Math. Soc. 130 (2002), 1285–1292.
  • J.J. Martínez, Cohomological dimension of discrete modules over profinite groups, Pacific J. Math. 49 (1973), 185–189.
  • L. Ribes and P. Zalesskii, Profinite groups, Springer-Verlag, Berlin, 2000.
  • L. Salce, Cotorsion theories for abelian groups, Sympos. Math. 23 (1979), 11–32.
  • J.P. Serre, Cohomologie Galoisienne, Lect. Notes Math. 5, Springer-Verlag, Berlin, 1997.
  • C. Studer-De Boer, Tate cohomology for profinite groups, Ph.D. Dissertation, Math. Wissen., Zürich, 2001.
  • M.L. Teply, Torsionfree injective modules, Pacific J. Math. 28 (1969), 441–453.
  • J. Xu, Flat covers of modules, Lect. Notes Math. 1634, Springer-Verlag, Berlin, 1996.