On 29 August 2014 10:27, Vincent Delecroix <[email protected]> wrote:
> 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 > ! http://en.wikipedia.org/wiki/Field_with_one_element > > -- > 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. > -- 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.
