This is mathematics.
Clear means get your paper, get your pen, and after some writing, you'll see its true. Clear does not mean it should be immediately obvious to you just by looking at it.

>>7645412
Um, duh?
That circled part is fucking basic algebra.

>>7645414

>>7645412
Wait shit nvm, it is obvious. Fuck.

They should have marked the products in parenthesis with appostrophes to show they are prime, or derivatives.

>>7645412
obviously f(squared)=-1 so f=i

>>7645466
>>7645471
It is because it says Div(X) is a free abelian group. That makes the properties circled obvious.

>>7645412
That's because you're a dumbass. Protip: think about what ord_a(f) stands for.

>>7645412
>(f*g) = (f) + (g)
what

>>7645849
Near [math]a[/math] the function [math]f[/math] is something like [math]f(x) = (x - a)^{ \text{ord}_a (f)} \cdot \text{something holomorphic}[/math], same with [math]g[/math]. So there product is
[math](f \cdot g) (x) = (x - a)^{ \text{ord}_a (f) + \text{ord}_a (g) } \cdot \text{something holomorphic} [/math].

You should see the addition of orders.

Why are you reading a book involving divisors if you haven't even done simple algebra?