# Z-Modules and Isomorphisms

Not what you're looking for?

(8) Prove that Hom_Z(Z/nZ,Z/mZ) is isomorphic to Z/(n,m)Z

##### Purchase this Solution

##### Solution Summary

Z-Modules and Isomorphisms are investigated.

##### Solution Preview

Proof:

We know, Z/nZ={0,1,...,n-1}, Z/mZ={0,1,...,m-1}. Let d=(n,m), then

Z/dZ={0,1,...,d-1}. As a group, Z/nZ,Z/mZ,Z/dZ are all cyclic groups.

So each homomorphism f from Z/nZ to Z/mZ is uniquely determined by f(1).

Let f_k in ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Probability Quiz

Some questions on probability

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.