Ring in the field of complex numbers
let k be a field. On the set
is defined the addition
and the multiplication
Proof that k[i] is a ring with the relations above.
I have a approach but I am not sure.
For proofing it, I guess I have to show that it is a commutative Group, that the multiplication is associative und the distributive laws.
So I want to start with the first. Showing that it is a Abel's group.
For the group I have to proof the existence of neutral elements, the existence of one inverse element, the associative law and the inner composition "+" must be commutative.
Okay, so far but how do I show this concretely?
all the best