A
finitely generated module is projective if and only if it is a
direct summand of...
A
finitely generated module is projective if and only if it is a
direct summand of a finitely generated free module. I am having
trouble grasping the "finitely generated" part.
Solutions
Expert Solution
P is R module then P is projective iff P is isomorphic to direct
summand of free R module.
a. Give an example of a finitely generated module over
an integral domain which is not isomorphic to a direct sum of
cyclic modules.
b. Let R be an integral domain and let
M=<m_1,...,m_r> be a finitely generated module. Prove that
rank of M is less than or equal to r.
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