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This question already has an answer here:

If $H$ is a ring and it has a finite non-zero characteristic $p$ then ring is finite.

I couldn’t any counter example for this claim. Can anyone help me please?

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marked as duplicate by Saad, Strants, John Omielan, Leucippus, rschwieb abstract-algebra Apr 4 at 2:04

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Just searching “positive characteristic infinite” yields the dupe and its duplicates. Please search first next time. $\endgroup$ – rschwieb Apr 4 at 2:06
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Consider the ring of polynomials with coefficients in $\mathbb{Z}/p$ it has characteristic $p$ and it is infinite.

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  • $\begingroup$ Thank you so much $\endgroup$ – user519955 Apr 3 at 22:53

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