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Math Help - nonzero torsion elements

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    nonzero torsion elements

    If R has zero divisors show that every nonzero R-module has nonzero torsion elements.
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  2. #2
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    Quote Originally Posted by zelda2139 View Post
    If R has zero divisors show that every nonzero R-module has nonzero torsion elements.
    so there exist nonzero elements r,s \in R such that rs=0. let M \neq (0) be an R-module and 0 \neq m \in M. if sm=0, then we're done. so suppose m'=sm \neq 0. then: rm'=(rs)m=0. \ \ \Box
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