International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 4, Pages 251-262
On Krull's intersection theorem of fuzzy ideals
1Department of Mathematics (Pure & Applied), Rhodes University, Grahamstown 6140, South Africa
2Department of Mathematics, University of Fort Hare, Alice 5700, South Africa
Received 11 May 2001
Copyright © 2003 V. Murali and B. B. Makamba. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.