Ideals in a ring

Let c be in a ring R and let I = {rc | r is in R}
Give an example to show that if R is not a commutative ring, then I need not be an ideal.

Can someone help me this?

Quote:

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Originally Posted by anlys

Let c be in a ring R and let I = {rc | r is in R}
Give an example to show that if R is not a commutative ring, then I need not be an ideal.

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For any and any , .
But may not be in .

Quote:

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Originally Posted by Byun

For any and any , .
But may not be in .

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Hello Byun,
Thanks for your input. Do you also have a particular example to show this?

Quote:

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Originally Posted by anlys

Let c be in a ring R and let I = {rc | r is in R}
Give an example to show that if R is not a commutative ring, then I need not be an ideal.

Can someone help me this?

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we have: let then