Question

In this exercise we want you to find all ring homomorphisms g from Z/72Z to Z/99Z. List all the possible values of g(1) when g is a ring homomorphism from Z/72Z to Z/99Z. The possible values are: Your last answer was interpreted as follows: {0,11,22,33} Notation: An element aˉ∈Z/kZ should be written as a number between 0 and k−1. Enter the answer as a set of numbers, for example: {0,1,4}.

Answer 1

To find all ring homomorphisms g from Z/72Z to Z/99Z and the possible values of g(1), we can use the Chinese Remainder Theorem.

Step-by-step explanation:

When finding all ring homomorphisms g from Z/72Z to Z/99Z, we need to find all the possible values of g(1). To do this, we need to find the elements in the range of the function g. In this case, we can use the fact that Z/72Z is isomorphic to Z/8Z×Z/9Z and use Chinese Remainder Theorem to find all possible values of g(1).

The possible values of g(1) are {0, 11, 22, 33}.