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## Homework Statement

In a ring with multiplicative identity, If x^n is in an ideal then is x also in the ideal? with n a natural number.

## The Attempt at a Solution

I can't find a proof. Which is likely to mean the statement is false?

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- Thread starter pivoxa15
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- #1

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In a ring with multiplicative identity, If x^n is in an ideal then is x also in the ideal? with n a natural number.

I can't find a proof. Which is likely to mean the statement is false?

- #2

radou

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I hope this works, since I'm a bit new to rings.

- #3

Dick

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Dick

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Eg. consider the ideal generated by 4 over the integers.

- #5

radou

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[This is a sign I should stop learning from various lecture notes, and turn to books. :uhh:]

- #6

matt grime

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No. It is a sign you should think about what you're reading.

- #7

matt grime

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I can't find a proof. Which is likely to mean the statement is false?

Just think about an example for a second. Like the simplest ring there is, the integers. Why didn't you do some examples to see if it was true?

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- #9

matt grime

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Good point. An example might be the ideal <2^2> in N which contains no element 2.

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