Reference : Division in modules and Kummer theory
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Physical, chemical, mathematical & earth Sciences : Mathematics
Division in modules and Kummer theory
Tronto, Sebastiano mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
[en] Injective modules ; Algebraic groups ; Elliptic curves
[en] In this work we generalize the concept of injective module and develop a theory of divisibility for modules over a general ring, which provides a general and unified framework to study Kummer-like field extensions arising from commutative algebraic groups. With these tools we provide an effective bound for the degree of the field extensions arising from division points of elliptic curves, extending previous results of Javan Peykar for CM curves and of Lombardo and the author for the non-CM case.

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