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CSteiner

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CSteiner

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mathwonk

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i looked in atiyah macdonald and found this.

zero divisor is a concept applied to a ring, while torsion element is the analogous concept applied to a module. i.e. in a ring A, x is a zero divisor if xy=0 for some y≠0 in A.

If A is a ring and M is an A module, an element z of m is a torison element if xz=0 for some non zero divisor x in A.

e.g. in an abelian group M, hence a module over the integers, an element z of M is torsion if and only if it generates a subgroup of finite order, i.e. if and only if nz = 0 for some n ≠0. in the integers there are of course no zero divisors (except 0).

zero divisor is a concept applied to a ring, while torsion element is the analogous concept applied to a module. i.e. in a ring A, x is a zero divisor if xy=0 for some y≠0 in A.

If A is a ring and M is an A module, an element z of m is a torison element if xz=0 for some non zero divisor x in A.

e.g. in an abelian group M, hence a module over the integers, an element z of M is torsion if and only if it generates a subgroup of finite order, i.e. if and only if nz = 0 for some n ≠0. in the integers there are of course no zero divisors (except 0).

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mathwonk

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CSteiner

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Okay, that makes sense, thanks!

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mathwonk

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