My textbook says that...(adsbygoogle = window.adsbygoogle || []).push({});

If M is a left R-module, then a submodule N of M...is an additive subgoup N of M closed under scalar multiplication: [tex]rn \in N[/tex] whenever [tex]n \in N[/tex] and [tex]r \in R[/tex].

So if we want to prove that something is a submodule, we need to show that...

1) It closed under scalar multiplication

2) The additive idenitity is in N

3) N is closed under additition

4) If x is in N, then so is its inverse

Right?

But, in the link that I attached, it only shows 1) and 3), right? Can anybody tell me why? Is the proof still considered complete?

Thanks in advance

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# A question about submodules

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