Determining whether homomorphism or not

[tgt]

It seems to be that the key to answering this question is in how elements are multiplied in the domain group. In other words, the type of multiplication in the domain group. What do you think?

 

[Office_Shredder]

Considering the definition of a homomorphism is that it preserves multiplicative structure, I imagine the key to figuring out whether it's a homomorphism lies in figuring out whether it preserves multiplicative structure.

 

[BryanP]

Considering the definition of a homomorphism is that it preserves multiplicative structure, I imagine the key to figuring out whether it's a homomorphism lies in figuring out whether it preserves multiplicative structure.

Definition of a homomorphism from a general perspective doesn't necessarily mean that it preserves a multiplicative structure.

A homomorphism doesn't even have to be using multiplication as the binary operation.

It depends also if you're dealing with let's say, rings, or groups (ring theory vs group theory).

Basically, a binary operation is homomorphic if it preserves structure from one domain to another.

You can do this by checking if the inverses, identity, and values from the binary operation coincide with the algebraic structure being mapped to.