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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Abstract

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

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

Dates
First available in Project Euclid: 18 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1492502544

Digital Object Identifier
doi:10.1216/RMJ-2017-47-2-429

Mathematical Reviews number (MathSciNet)
MR3635368

Zentralblatt MATH identifier
06715755

Subjects
Primary: 18G25: Relative homological algebra, projective classes

Keywords
Torsion free discrete module cotorsion module

Citation

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. https://projecteuclid.org/euclid.rmjm/1492502544


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