ALTERNATIVE PROOF OF HILBERT BASIS THEOREM - MESYA (NIM: 20107077), ADI
Hilbert Basis theorem was proven by direct proof in Samuel and Zariski. This direct proof is using maximum condition and finite basis condition. The alternative proof which will be discussed rigorously in this project is an indirect proof written by Caruth. Homomorphism theorem and Zorn lemma is needed in this indirect proof. Zorn lemma gives a fact that in a non-Noether ring under inclusive relation, the ideal set which not generated finitely has maximal element.