- #1

Bashyboy

- 1,421

- 5

## Homework Statement

No problem statement.

## Homework Equations

## The Attempt at a Solution

Suppose that ##R## is a ring and ##f : R \to R## is an additive group homomorphism. Is the following a way of extending ##f## to a ring homomorphism? Let ##\varphi : R \to R## and define ##\varphi(r) = f(r)## if ##r \in R - R^\times##, where ##R^\times## is the group of units, and ##\varphi(rs) = f(r) f(s)## if ##r,s \in R^\times##...Something about that definition doesn't feel right. Or perhaps ##\varphi(a+b) = f(a) + f(b)## and ##\varphi(ab) = f(a) f(b)##...I suspect that that isn't well-defined...I could use some help.