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

On Fri, 1 Apr 2005, Matt Gutting wrote:

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'

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?

Or am I missing something?

You're surprise that when you go to a different country,
that everything is different?

2 and 4 in Z[1/2] are units, ie have multiplicative inverse.
All non-zero rationals are units in Q.
In Z, the only units are +-1 and they are coprime.
You have noticed all units of a ring are coprime.


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