Prove that there exist at most 2 non-isomorphic fields of order 4.
Not what you're looking for?
Prove that there exist at most 2 non-isomorphic fields of order 4.
Purchase this Solution
Solution Summary
It is proven that there exist at most 2 non-isomorphic fields of order 4.
Solution Preview
Proof:
We know that F=Z2={0,1} is a field with order 2, f(x)=x^2+x+1 is an irreducible polynomial
in F. Then F[x]/(f(x))=F[x]/(x^2+x+1)={0,1,x,x+1} is a field with order 4.
Because there is ...
Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
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.