Find all maximal ideals in Z8... 1. The problem statement, all variables and given/known data http://gyazo.com/e292522bc3d99584d5abb55826b4a50f 2. Relevant equations Some definitions. http://gyazo.com/f095ef61ecc9806c8f6a95fa99dad6fb I was also thinking about using a lattice of ideals to show this. 3. The attempt at a solution Okay, when I draw out the ideal lattice for these, it's obvious to see which ideals are maximal. For part a, b, and c. a) For Z8, <2> is maximal. b) For Z10, <2> and <5> are maximal. c) For Z12, <2> and <3> are maximal. d) Requires a proof. Lattice fails. My question is, how would I argue this without the aid of a lattice for a, b and c?