I want to prove that every field has exactly 2 ideals.
I know that the two ideals are $0$ and the whole set itself. That is clear to me. I am a little unsure how to prove it though.
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If it's not the zero ideal, it contains a nonzero number. In a field, every nonzero number is ... – Daniel Fischer Sep 25 '13 at 00:43
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Hmm I can see how the whole set is an ideal but I am still unsure of zero. Why does an ideal have at least the zero element? – Steve Thomas Sep 25 '13 at 01:15