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Here is a question about abastract algebra

Let A be a nonzero commutative ring such that any ring homomorphism from A to any nonzero ring B is one-to-one. Show that A is a field.

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closed as off-topic by Kenny Wong, Najib Idrissi, user26857, Namaste, Servaes Mar 30 '17 at 14:26

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Hint: kernels are ideals, and any ideal is the kernel of some map.

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  • $\begingroup$ This answer is perfect imo, I don't know why someone would downvote $\endgroup$ – Alex Mathers Mar 30 '17 at 9:22