True or FalseLabel each of the following statements as either true or false.1. A ring homomorphism from a ring R to a ring R' must preserve both ring operations.2. If a homomorphism exists from a ring R to a ring R', then R' is called a homomorphicimage of R.

Let us analyze each statement: 1. A ring homomorphism from a ring R to a ring R′ must preserve both…

Answered: True or False Label each of the…

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 2TFE: True or false Label each of the following statements as either true or false. If a homomorphism...

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True or False Label each of the following statements as either true or false. 1. A ring homomorphism from a ring R to a ring R' must preserve both ring operations. 2. If a homomorphism exists from a ring R to a ring R', then R' is called a homomorphic image of R.