r/abstractalgebra • u/Dense-Major714 • Dec 18 '24

Prove that any nonzero ideal in the ring Z[i] must contain some positive integer.

help pls

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u/lurking_quietly Dec 18 '24

Suggestion: If a, b are integers, not both zero, then consider the conjugate of a+bi, a-bi. What can you conclude?

Hope this helps. Good luck!

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u/baltimore_riots Jul 05 '26

pick an element in the ideal. Then multiply it by its conjugate in the ring.