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International Journal of Mathematics and Mathematical Sciences - Volume 2003 2003, Issue 4, Pages 251-262



Department of Mathematics Pure & Applied, Rhodes University, Grahamstown 6140, South Africa

Department of Mathematics, University of Fort Hare, Alice 5700, South Africa

Received 11 May 2001

Copyright © 2003 Hindawi Publishing Corporation. 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.

Abstract

We deal with Krull-s intersection theorem on the ideals of acommutative Noetherian ring in the fuzzy setting. We firstcharacterise products of finitely generated fuzzy ideals in termsof fuzzy points. Then, we study the question of uniqueness andexistence of primary decompositions of fuzzy ideals. Finally, weuse such decompositions and a form of Nakayama-s lemma to provethe Krull intersection theorem. Fuzzy-points method on finitelygenerated fuzzy ideals plays a central role in the proofs.





Autor: V. Murali and B. B. Makamba

Fuente: https://www.hindawi.com/



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