Re: Coprimeness - I think I'm confused, but I'm not sure

Matt Gutting <matthewdba@xxxxxxxxxxx> writes:
>
> In light of some of the comments in the JSH threads
> involving coprimeness and Z[1/2]:
>
> If the definition of coprimeness is something like:
>
> To say that 'p and q are coprime in a ring' is to say
> 'there exist a,b in the ring with ap + bq = 1'

Yes, that is probably the most common definition of 'coprime'
but be aware there are also many others in use, see my post [1],

> then wouldn't 2 and 4 (or any powers of 2) be coprime in Z[1/2]?
> Or, more strongly, are any 2 (non-zero) rationals coprime in Q?

Yes a unit (invertible) elt is always coprime to any other elt
for every notion of coprime I'm aware of. E.g. it is true for
the above notion since a c = 1 => a c + b 0 = 1

--Bill Dubuque

[1] http://groups-beta.google.com/group/sci.math/msg/26729f0cd82b5866
http://google.com/groups?selm=y8z4qyo4oay.fsf@xxxxxxxxxxxxxxxxx
.

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