Modern algebra
Not what you're looking for?
I am stuck with this question.
If phi : F -> R is a nonzero homomorphism from a field F to a ring R, show that phi is one-to-one (Hint: recall that for a ring homomorphism, phi is one-to-one if and only if Ker(phi)={0}. )
Can you help with this?
Many thanks in advance
Purchase this Solution
Solution Summary
This solution is comprised of a detailed explanation to show that phi is one-to-one.
Solution Preview
Proof:
We do not consider the trivial case: phi(a)=0 for any a in F. In this case, phi is not ...
Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
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.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.