Re: e idempotent, e+1 unit

On Sun, 28 Sep 2008, Bill Dubuque wrote:

William Elliot <marsh@xxxxxxxxxxxxxxxxxx> wrote:
On Sun, 28 Sep 2008, Kobu wrote:

"e idempotent is part of a ring which has rationals as subring
=> 1+e is a unit"

Huh? What are you saying? What ever it is, it's much confused.
How is an element a part of a ring? My translation is:

If e is an idempotent in a ring which has a subring isomorphic to Q,
then 1 + e is a unit. That is false.

Let R = Q x Z_6. Let e = (1,3); ee = e; 1 = (1,1)
1 + e = (2,4). Is 1 + e a unit? No,

No, Q isn't a subring of R. Subrings must have same 1 = (1,1).

Definitions upon this detail vary.
Does a ring have to have a unit or not?
Does a subring have to include the multiplicative identity of the ring?

To be clear, one needs to be explict:
ring, ring with unit, subring, subring with unit,
subring with ring's multiplicative identity.

.

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