Hi:

Let be a ring with unity and assume are the identity elements for addition and multiplication respectively in . Can be true? I think the only way is . Any hint will be welcome. Regards.

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- November 25th 2009, 07:12 PMENRIQUESTEFANINIRings with 0 = 1.
Hi:

Let be a ring with unity and assume are the identity elements for addition and multiplication respectively in . Can be true? I think the only way is . Any hint will be welcome. Regards. - November 25th 2009, 07:24 PMtonio
- November 25th 2009, 08:42 PMShanks
Yes, If 0=1 in R, then R is trivially {0}, containning only the element 0.

- November 26th 2009, 01:07 AMSwlabr
- November 26th 2009, 06:34 AMENRIQUESTEFANINI
Thanks, thanks. I'd seen definitions requiring the ring to have two or more elements, but I'd never seen the same thing specified as zero and one being diferent elements. This seemed a bit odd to me. Now I see that authors use these two constrains interchangably. Thanks again,

Enrique.