# Difference between torsion and zero divisor

I'm not understanding what the difference is between a zero divisor and a torsion element of a module. My best guess is that the torsion elements are "vectors" and zero divisors are scalars. This seems wrong to me, but I've looked over the definitions (Wikipedia) for a few days now and I can't spot the difference.

• Your best guess is right. A zero-divisor is a torsion element in the ring itself. – darij grinberg Jul 29 '15 at 2:18
• I get the feeling you didn't read the definitions very carefully: how could they be considered the same? They're of a similar flavor, of course... but the definitions aren't identical... – rschwieb Jul 30 '15 at 17:25

• one definition of a torsion element of an $R$ module is that its annihilator in $R$ is an essential ideal.