3. Let A be a -module, T(A)= {aA| za=0 for some0z }. a) Show that T(A)...

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3. Let A be a -module, T(A)= {aA| za=0 for some0z }. a) Show that T(A) is a submodule of A. b) Prove that if A is divisible, then T(A) is a direct summand of A. 3. Let A be a -module, T(A)= {aA| za=0 for some0z }. a) Show that T(A) is a submodule of A. b) Prove that if A is divisible, then T(A) is a direct summand of A.

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a To show that TA is a submodule of A we need to demonstrate the following 1 TA is nonempty 2 TA is ... View the full answer