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

Bill Dubuque wrote: 
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


Thanks Bill. I think I have it straight.

Matt
.

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