2014-08-29 10:51 UTC+02:00, John Cremona <[email protected]>:
> 1 is definitely not a prime power.  It's basically the same reason that 1
> is not a prime.
>
> Some reasons: (1)  positive integers are uniqely products of prime powers
> (with 1 being the empty product!)  Uniqueness would fail if 1 were allowed.
> (2) a positive integer n is a prime power iff nZ is a primary ideal of Z
> (that got you 2 marks in an exam I set this year), and the definition of
> primary ideal (as with prime ideal) explicitly requires the ideal to be
> proper.
(3) q is a prime power iff there exists a field of cardinality q

-- 
You received this message because you are subscribed to the Google Groups 
"sage-nt" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to [email protected].
To post to this group, send an email to [email protected].
Visit this group at http://groups.google.com/group/sage-nt.
For more options, visit https://groups.google.com/d/optout.

Reply via email to