Ideals

• When Do Finitely Generated Prime Ideals Imply a Noetherian Ring?
  For a commutative ring with identity, being Noetherian is equivalent to every prime ideal being finitely generated; here is the proof and key distinction.
• How to Make Addition and Multiplication Tables for a Ring or Ideal
  Build ring and ideal operation tables by applying the inherited operations to each pair; see a complete example using Z4 and its ideal {0, 2}.