International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 4, Pages 251-262
doi:10.1155/S0161171203013097
On Krull's intersection theorem of fuzzy ideals
V. Murali1
and B.B. Makamba2
1Department of Mathematics (Pure \& Applied), Rhodes University, Grahamstown 6140, South Africa
2Department of Mathematics, University of Fort Hare, Alice 5700, South Africa
Abstract
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-points method on finitely generated fuzzy ideals plays a central role in the proofs.