On Mar 14, 10:29 am, Avishek Adhikari <avishek....@gmail.com> wrote: > I fully agree with you. But it will not certainly give all prime ideals!
Yes it will. The number of prime ideals of Z/nZ is exactly the number of prime divisors of n. In general the prime ideals of R/I (where R is a commutative ring and I an ideal) are of the form P/I where P is a prime ideal of R which contains I, and P <--> P/I is a bijection. In this case, R=Z, I=nZ so P has to be pZ where (1) p is prime, so that P is a non-zero prime ideal and (2) p divides n, so that P contains I. John Cremona > > On Sun, Mar 13, 2011 at 9:30 PM, John Cremona <john.crem...@gmail.com>wrote: > > > > > This is not a computational question at all but an easy exercise. > > There is one prime ideal for each prime factor p of n, namely pZ/nZ. > > See any book on elementary ring theory! > > > John Cremona > > > On Mar 12, 11:41 pm, Avishek Adhikari <avishek....@gmail.com> wrote: > > > Hello, > > > I shall be glad, if you kindly send the help towards finding the > > solution > > > of the following problem using sage: > > > > In Z_n (the ring of integers modulo n), find all prime ideals. > > > > Waiting for your reply. > > > Best regards, > > > Avishek > > > -- > > To post to this group, send email to sage-support@googlegroups.com > > To unsubscribe from this group, send email to > > sage-support+unsubscr...@googlegroups.com > > For more options, visit this group at > >http://groups.google.com/group/sage-support > > URL:http://www.sagemath.org > > -- > Dr. Avishek Adhikari > website :http://imbic.org/avishek.html > Secretary, IMBIChttp://www.imbic.org/forthcoming.html > Faculty Member, Dept. Of Pure Mathematics, > University of Calcutta, > 35 Ballygunge Circular Road, > Kolkata 700019, > West Bengal, India. > Ph no. (M) (0) 9830794717 -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
