# Re: prime numbers and African artifact

lefty@eexi.gr
20 Jul 1995 12:21:34 GMT

Daniel Kian Mc Kiernan <dmckiern@weber.ucsd.edu> wrote:
>
>
> I'm familiar with three definitions of "prime number".
>
> [1] A positive integer divisible only by itself and by 1.
>
> [2] Same as [1] except that the number must also be greater than 1.
>
> [3] Same as [1] or [2] except that the number must also be greater
> than 2.
>
> For my part, I don't care for definitions [2] or [3].
>
> It's always Dark. Light only hides the Darkness.
>
> Daniel Kian Mc Kiernan (619) 535 - 0546
> athanatos@UCSD.edu 132.239.147.2 <75013,676>
>

What about -1? 3 is divisible by 1, -1, 3 and -3.

Primes can be defined in any ring, the definition if I remember correctly is:

R is a ring, p \in R, p is prime \iff the ideal I generated by p is maximal.
That is every proper ( non R ) ideal containing p contains I.

Lefty Kreouzis -- lefty@eexi.gr