By the Chinese Remainder Theorem, there is a ring isomorphismy: Z/10Z ~ Z/2Z × Z/5Z,(a) Write out this isomorphism explicitly, in terms of elements.(b) What are the units in Z/10Z? How do these correspond to units in Z/2Z × Z/5Z?a + 10Z → (a + 2Z, a + 5Z)

Answer Explanation:Step 1: Step 2: Step 3: Step 4:

Answered: By the Chinese Remainder Theorem, there…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter7: Real And Complex Numbers

Section7.2: Complex Numbers And Quaternions

Problem 51E: An element in a ring is idempotent if . Prove that a division ring must contain exactly two...

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By the Chinese Remainder Theorem, there is a ring isomorphism y: Z/10Z ~ Z/2Z × Z/5Z, (a) Write out this isomorphism explicitly, in terms of elements. (b) What are the units in Z/10Z? How do these correspond to units in Z/2Z × Z/5Z? a + 10Z → (a + 2Z, a + 5Z)