Purchase Solution

Constructing a field with p^2 elements

Not what you're looking for?

Ask Custom Question

How can we construct a field having p^2 elements, p being an odd prime. Please explain in detail.
(Hint: Think about polynomial rings.)

Purchase this Solution

Solution Summary

We explain the process of constructing a field with p^n elements, p being an odd prime and apply it to the example with n=2.

Solution Preview

There is a standard way of constructing a field with p^n elements, for a prime number p.

You start with Z_p = Z/pZ, which is a field with p elements (integers modulo p) and consider the splitting field of the polynomial f(x) = x^{p^n} - x over Z_p.

Such a polynomial has precisely p^n distinct roots over Z_p, since its derivative ...

Purchase this Solution


Free BrainMass Quizzes
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.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability

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.