by Artusartos
Tags: submodules
 P: 247 My textbook says that... If M is a left R-module, then a submodule N of M...is an additive subgoup N of M closed under scalar multiplication: $$rn \in N$$ whenever $$n \in N$$ and $$r \in R$$. 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 Attached Thumbnails