Consider the group ring . How many module structures, up to isomorphism, does admit? Do the same for . With this information, calculate in such cases.

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#
module theory

# Module structures

# Freedom

Consider the group ring . How many module structures, up to isomorphism, does admit? Do the same for . With this information, calculate in such cases.

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Every morphism of abelian groups vanishing on is identically zero.

Use this fact to prove that is not a free abelian group.