What do you call this homomorphism?

[tgt]

f:A->A but f(a) does not equal a for all a in A.

 

[waht]

Endomorphism?

 

[Jang Jin Hong]

If set of all homomorphism is denoted as U,
and identity mapping is denoted as I

That is complementary set of identity map.
denoted as U-I

 

[HallsofIvy]

So you have a "set of homomorphisms" minus a single homomorphism? U- {I} would make more sense. But I would interpret "does not equal a for all a in A" as meaning f(a) is NEVER equal to a.

 

[geor]

I am confused, too.
A group homomorphism always
maps 1 to 1, so...

 

[tgt]

So you have a "set of homomorphisms" minus a single homomorphism? U- {I} would make more sense. But I would interpret "does not equal a for all a in A" as meaning f(a) is NEVER equal to a.

fair point. It's probably an endomorphism.

 

[tgt]

Endomorphism?

that seems right.