I'm looking to prove that the following conditions are equivalent for an ideal I in a ring R.

1) 1 is in A

2) A contains a unit

3) A = R

thanks

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- Dec 15th 2008, 09:10 AMchrisneedshelpRings - Ideals - Equivalent statements?
I'm looking to prove that the following conditions are equivalent for an ideal I in a ring R.

1) 1 is in A

2) A contains a unit

3) A = R

thanks - Dec 15th 2008, 10:34 AMclic-clac
I guess that A means I :)

So since is a unit, is obvious.

If contains a unit , then, by ideal's definition, so . because of ideal's definition. So .

Finally, , therefore .