Answered: For each point a∈R of the ring ≺R,+,⋅≻,…

For each point a∈R of the ring ≺R,+,⋅≻, the mapping θa:≺R,+,⋅≻→≺R,+,⋅≻ defined by θa(x)=a⋅x, ∀x∈R is a one-to-one ring homomorphism. True False

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

For each point a∈R of the ring ≺R,+,⋅≻, the mapping θa:≺R,+,⋅≻→≺R,+,⋅≻ defined by

θa(x)=a⋅x, ∀x∈R

is a one-to-one ring homomorphism.

True

False

Expert Solution

Step 1: Example taking

Consider R = Z₆

Then, we know obviously that (R, +, . ) is a ring.

Consider a = 2.

So,

θ₂(x)=2x

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

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