ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 15 Mar 2011 10:13:32 -0500Prime ideals and "Point on Spectrum"http://ask.sagemath.org/question/8003/prime-ideals-and-point-on-spectrum/The spectrum of the ring of integers $\mathbb{Z}$ consists of the prime ideals, i.e. $Spec(\mathbb{Z}) = \cup_{p \space prime}p\mathbb{Z} \cup (0)$.
i1: S = Spec(ZZ)
i2: nZ = ZZ.ideal(6)
i3: S(nZ)
o3: Point on Spectrum of Integer Ring defined by the Principal ideal (6) of Integer Ring
i4: nZ.is_prime()
o4: False
Obviously, nZ is not a prime ideal, as 6 is composite. Hence by definition, it is not in $Spec(\mathbb{Z})$. So what does "Point on Spectrum" means exactly in Sage?
ThanksWeaamTue, 15 Mar 2011 10:13:32 -0500http://ask.sagemath.org/question/8003/