An element m of the R-module M is called a torsion element if rm=0 for some non-zero element r∈R .
(i) Prove that if R is an integral domain then T or (M) , the set of torsion elements of M , is a submodule of M (called the torsion submodule of M).
(ii) Give an example of a ring R and an R-module M such that T or(M) is not an R-submodule.
(iii) If R has zero-divisors, show that every non-zero R-module has non-zero torsion elements.
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