Purchase Solution

Homomorphism

Not what you're looking for?

Ask Custom Question

Prove that for in H,
Thus, N is a homomorphism from onto the positive real numbers.

See attached file for full problem description.

Attachments
Purchase this Solution
Solution Summary

This is a proof regarding a homomorphism onto positive real numbers.

Solution Preview

We can solve this problem in several ways: we could check directly that the relations hold, or in order to simplify the computations we can use the other problem (that I already solved) that was included in this set of problem, that said that to any a in H we can associate a matrix A_a, which we showed that has the properties that det(A_a)=N(a)^2 (I will use the notation x^2 for the square of x), and ...

Purchase this Solution
Free BrainMass Quizzes
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.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

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

View More Free Quizzes
Related BrainMass Solutions

  • Prove that the Kernel of a homomorphism is a subspace.

    137567 Prove that the Kernel of a homomorphism is a subspace. Prove that the Kernel of a homomorphism is a subspace.

  • Homomorphism of a Group and Kernel of the Homomorphism

    64420 Group Theory :Homomorphism of a Group: Verify if the mapping defined is a homomorphism and in that case in which it is homomorphism,determine the Kernel:G is the group of non-zero real numbers under multiplication, ¯G = G, phi(x) = x^2 all x belongs

  • Homomorphism of a Group and Kernel of the Homomorphism

    Kernel of the Homomorphism Verify if the mapping defined is a homomorphism and in that case in which it is homomorphism, determine the Kernel: G is any abelian group and ¯G = G, phi(x) = x^5 all x

  • Group and ring homomorphisms

    Is this function a Homomorphism? a) Does 1:22 :22 where 1(a1,a2) = (a1,0) define a group homomorphism? a ring homomorphism? Prove your answers.

  • Group homomorphisms

    Homomorphism Problem 1: Solution: Any homomorphism µ : Zn -> Zk is completely determined by µ([1]n), and this must be an element [m]k of Zk whose order is a divisor of n.

  • Fields and homomorphisms

    Second, I claim that is a ring homomorphism. For any , we have Thus is a ring homomorphism. Third, for any , let , then we have So is an identity map on . Therefore, is a -algebra homomorphism.

  • Solve: Onto Homomorphisms

    a) Show that varphi: Z_2 --> Z_2 defined by varphi(x) = x^2 is a homomorphism. b) Show that {}: Z_3 --> Z_3 defined by {}(x) = x^3 is a homomorphism. c) Show that theta: Z_4 --> Z_4 defined by theta(x) = x^4 is not a homomorphism.

  • Identity Element Preserved in a Homomorphism

    38310 Identity Element Preserved in a Homomorphism Let ... be a homomorphism of a group ... into a group... . Show that if is the identity element of... , then is the identity element... in ... .

  • Problems in Group Theory

    455433 Problems in Group Theory: Homomorphism Let G_1 and G_2 be groups and ?:G_1?G_2 a map. Which of the following is a group homomorphism? Explain your answers. If ? is a homomorphism, describe the kernel and the image of ?. a) G_1=C_4=?

  • Homomorphism and First Isomorphism Theorem

    According to the first homomorphism theorem, we have . Done. Homomorphism and First Isomorphism Theorem are investigated. The solution is detailed and well presented.

View More Related Solutions