Exercise 36. Prove the above theorem. Hint: some pieces have been done in earlier theorems and exercises. For example, if you want to show [0] is the additive identity, you only need to show [a]+[0] = [a] since [0]+[a] = [a]+[0] from an earlier theorem.
Exercise 36. Prove the above theorem. Hint: some pieces have been done in earlier theorems and exercises. For example, if you want to show [0] is the additive identity, you only need to show [a]+[0] = [a] since [0]+[a] = [a]+[0] from an earlier theorem.
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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Prove Theorem 20.
![Theorem 20. Let m be a positive integer. Then Zm is a commutative ring
with additive identity [0] and multiplicative identity [1]. The additive inverse
of (a] is [-a).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F946be153-534b-47e9-b2ae-1271a90bac9b%2Fc1f258e6-f7d6-4474-96d1-cca2f7bbcd2e%2Fum72jrl_processed.png&w=3840&q=75)
Transcribed Image Text:Theorem 20. Let m be a positive integer. Then Zm is a commutative ring
with additive identity [0] and multiplicative identity [1]. The additive inverse
of (a] is [-a).
![Exercise 36. Prove the above theorem. Hint: some pieces have been done
in earlier theorems and exercises. For example, if you want to show [0] is the
additive identity, you only need to show [a]+[0] = [a] since [0]+[a] = [a]+[0]
from an earlier theorem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F946be153-534b-47e9-b2ae-1271a90bac9b%2Fc1f258e6-f7d6-4474-96d1-cca2f7bbcd2e%2F03g3lx_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 36. Prove the above theorem. Hint: some pieces have been done
in earlier theorems and exercises. For example, if you want to show [0] is the
additive identity, you only need to show [a]+[0] = [a] since [0]+[a] = [a]+[0]
from an earlier theorem.
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