Definition talk:Field Homomorphism

I propose to change the definition Field Homomorphism to preserve multiplicative identity.

Fields are unital rings, so it seems strange to not force a field homomorphism to be a unital ring homomorphism. Under this definition, there is an annoying edge case of the trivial homomorphism (all others are injective), which doesn't behave well and nobody cares about anyway...

If nobody responds within a few days I will change the definition and related theorems. 12AbBa (talk) 04:26, 5 November 2023 (UTC)

No, please don't. The definition as it stands here is sourced directly from the cited work. The "annoying case" which "nobody cares about" is taken care of (also in that work) in Field Homomorphism is either Trivial or Injection.

However, if you can find a source work which you can reference, then please feel free to add a second definition, using the standard form of multiple definitions.

If you cannot find such a source work, please leave it alone. --prime mover (talk) 07:52, 5 November 2023 (UTC)