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My textbook says that...
If M is a left Rmodule, 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
If M is a left Rmodule, 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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