What do you call this homomorphism?

1. Oct 15, 2008

tgt

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

2. Oct 15, 2008

waht

Endomorphism?

3. Oct 15, 2008

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

4. Oct 16, 2008

HallsofIvy

Staff Emeritus
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.

5. Oct 16, 2008

geor

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

6. Oct 17, 2008

tgt

fair point. It's probably an endomorphism.

7. Oct 17, 2008

tgt

that seems right.