A homomorphism is a transformation of a first set into a second set that preserves in the second set the relations between elements of the first set.
The expression “relations between elements in the first set” is vague. Once we show an example you will see that this is a first set and a first multiplication and a second set and a second multiplication.
In this usage, multiplication on two set members results in a set member.
Appendix Z
As a certain something above was typed, a horror dawned on us: if we have an operation on two elements of a set and the result is an element of the set, the general word for that is addition. The word multiplication carries with it the idea of a something else operating on something from the set producing something from the set.
We profusely apologize for this.
They probably call the multiplication because they want to write sentences like:
(a)(b)=(c)
AB=C
Vectoreverything 