Re: prime....

On Thu, 21 Jul 2005, mina_world wrote:

> for all ab in Z,
> if p|ab, p|a or p|b. => integer p>1 is prime.
>
That's often the definition of prime.
p in N\1, for all a,b in Z, (p | ab ==> p|a or p|b)
==> p irreduciable.
If p = rs, then p | rs.
p|r or p|s; r /= 0 /= s
case p|r: some k with r = pk = rsk; sk = 1; s is unit
case p|s: similar. Put it all together now, p is irredicable.

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