If you find any mistakes, please make a comment! Thank you.

## Exhibit all of the ring homomorphisms from the cartesian square of the integers to the integers

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.5 Describe all ring homomorphisms from $\mathbb{Z} \times \mathbb{Z}$ to $\mathbb{Z}$. In each case, describe the kernel…