# a proof for krull schmidt theorem

I'm trying to understand the proof of this theorem:

which is:

I don't inderstand the highlighted lines, can somenone explain why this occur?

for the first I think it must be the direct sum

for the second, I don't see how he identified the couple of morphisme to one morphisme for the third It is not clear for me how it is impossible, I think there are some lines omitted

for the last one I think it must be the sum not the product

• In order for someone to help you properly, you must explain why you don't undertand the highlighted lines. You surely must have given it some thought, so explain your thoughts and explain either why you think the lines are false, or explain what's blocking you from agreeing with those lines Commented May 21, 2022 at 10:48
• Otherwise any answerer-to-be will have literally no idea which problems to address. The title should also be clarified, e.g. a specific statement of one of the issues that you are having Commented May 21, 2022 at 10:48
• for the first I think it must be the direct sum Commented May 21, 2022 at 10:55
• Don't tell me that, tell the post that! Make the edits with all detail that you need to provide Commented May 21, 2022 at 10:56
• Good for editing, but I think you should add some more edits. Your explainers are incredibly brief. Why do you think it must be the direct sum? Why must it be the sum and not the product? Literally, it is unlikely you'll get a satisfying answer unless you outline what you want help with. It is in your best interest to make these edits Commented May 21, 2022 at 11:41