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Basically I'm playing around with modules at the moment, and I can't work out why we cant have the group of integers as an F-module (F a field), where the left action is the identity.

i.e F x Z ----> Z

where we have f.z = z

f in F, z in Z

If this were possible, then Z would be a vector space wouldn't it, this is probably a stupid question but would be grateful if somebody could point out where I'm going wrong, i've been trying to work it out for hours.

Thanks!

C

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# Having trouble working with modules

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