$R$ - commutative ring. $I$ - ideal of that ring. Prove that ring $R/I$ - is a field and only if $I$ $!=$ $R$ and any proper ideal in $R$ does not contain $I$
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What have you tried? See How to ask a good question. – Ѕᴀᴀᴅ May 06 '20 at 10:24
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The ideal of field is only the whole field and $(0)$. – Zoe May 06 '20 at 10:30
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Let $R$ be a commutative ring and $k$ be a field. Assume $\phi\colon R\to k$ is a ring homomorphism and onto.
What can you conclude about $\ker\phi$ fomr the fact that $\phi$ is not the zero homomorphism?
What is the relation between ideals in $R$ containing $\ker\phi$ and ideals in $k$?
Hagen von Eitzen
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