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

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 12E: 12. Consider the mapping defined by . Decide whether is a homomorphism, and justify your decision.

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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

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