Let R be an integral domain and M an R-module. An element x = M is...

 

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Let R be an integral domain and M an R-module. An element x = M is said to be a torsion element if there is a r ER such that r 0 and rx = 0. 1. Show that Mtor M. = {m Mm is a torsion element} is a submodule of == 2. Show that the R-module N = M/Mtor has no non-zero torsion element. Let R be an integral domain and M an R-module. An element x = M is said to be a torsion element if there is a r ER such that r 0 and rx = 0. 1. Show that Mtor M. = {m Mm is a torsion element} is a submodule of == 2. Show that the R-module N = M/Mtor has no non-zero torsion element.