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I am focused on Section 4.2: Noetherian and Artinian Modules and need some help to fully understand the proof of part of Proposition 4.2.7 ... ...

Proposition 4.2.7 reads as follows:https://www.physicsforums.com/attachments/8208In the above proof by Paul Bland we read the following:

" ... ... and since each \(\displaystyle M_i\) is isomorphic to a submodule of \(\displaystyle \bigoplus_{ i = 1 }^n M_i\) ... ... "Can someone please explain to me how/why each \(\displaystyle M_i\) is isomorphic to a submodule of \(\displaystyle \bigoplus_{ i = 1 }^n M_i\) ... ... ?

Do we know what the submodule is ... ?

Help will be appreciated ...

Peter