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How many distinct cosets are there in the factor ring Z[i] / <3 + i>? Explain your answer.

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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How many distinct cosets are there in the factor ring Z[i] / <3 + i>? Explain your answer.

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Where does (3+i)(3-i) come from? I know <3+i> means a cyclic group but 3+i can't turn into 3-i with a positive integer exponent.

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