I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K).(adsbygoogle = window.adsbygoogle || []).push({});

I need help with the proof of Lemma 1.2.21 ...

Lemma 1.2.21 and its proof reads as follows:

In the above text (in the proof) by Berrick and Keating we read the following:

"... ... Any submodule properly containing ##X'## must contain ##x_0##, also, so ##X'## is maximal among all the proper submodules of ##M##. ... ...

My first question is ... why must any submodule containing ##X'## also contain ##x_0## ... ?

My second question is ... why does ##X##' containing ##x_0## allow us to conclude that

##X'## is maximal among all the proper submodules of ##M##. ... ... ?

Hope someone can help ...

Peter

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# I Finitely Generated Modules ... another question

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