Problem 2.8.4. Let k be a fixed positive integer. Let an be the integer ān =an (mod k) for an E Z.1. Prove that o : Z[a] → Zk[x] defined by ana" ++ao + ānx" +.+ãois a ring homomorphism.2. Prove that GCD (an;,ao) = GCD (an,...

Given : Let k be a fixed positive integer and a¯n ≡ an mod k for an ∈ ℤ To prove : (1) ϕ : ℤx →…

Answered: Problem 2.8.4. Let k be a fixed…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 17E: 17. Suppose is a ring with positive characteristic. Prove that if is any ideal of then is a...

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Problem 2.8.4. Let k be a fixed positive integer. Let an be the integer an an (mod k) for an EZ. 1. Prove that o: Z[x] → Zk[x] defined by anx" +...+ ao →ānx² + ··· +ão is a ring homomorphism. 2. Prove that GCD (an,,ao) = GCD (an, ‚ão)