A univariate polynomial ring over a field is a PID, but not if its over a general ring. E.g. <2,x> in ZZ[x] can't be generated by a single polynomial.
On Saturday, January 26, 2013 10:45:18 PM UTC, Charles Bouillaguet wrote: > > If I am not mistaken, any ideal I = <f_1, …, f_r> of R[x] is spanned by a > **single** polynomial (which is the gcd of the f_i). So, in your examples, > the ideal spanned by x^2 and x^2+x+1 is in fact R[x], because their gcd is > one. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To post to this group, send email to sage-devel@googlegroups.com. To unsubscribe from this group, send email to sage-devel+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel?hl=en.
