On Krull's intersection theorem of fuzzy ideals (Q1864274)

Summary: We deal with Krull's intersection theorem on the ideals of a commutative Noetherian ring in the fuzzy setting. We first characterise products of finitely generated fuzzy ideals in terms of fuzzy points. Then, we study the question of uniqueness and existence of primary decompositions of fuzzy ideals. Finally, we use such decompositions and a form of Nakayama's lemma to prove the Krull intersection theorem. Fuzzy-point methods on finitely generated fuzzy ideals play a central role in the proofs.