Well, first of all I'm not quite sure If I'm posting my question in the right section so forgive me if it's in the wrong section. I'm studying module-theory on my own and in the chapter I'm in the book is discussing tensor product of modules (actually I decided to read this book only because of this chapter xD), there's a theorem in the book that is about taking the tensor product of a given exact sequence (the book doesn't say it this way, but this is how I memorize the whole theorem because It's kinda like that). I've attached the theorem and its proof, the book that I'm reading is not in English so I was forced to translate everything into English, if there are points that are ambiguous tell me to clarify them.(adsbygoogle = window.adsbygoogle || []).push({});

I understand the whole proof, except two parts that I've highlighted them in red in the pdf.

Thanks in advance

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# Could someone explain this to me please?

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