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On Krull's intersection theorem of fuzzy ideals

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  • V. Murali
  • B. B. Makamba

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.

Suggested Citation

  • V. Murali & B. B. Makamba, 2003. "On Krull's intersection theorem of fuzzy ideals," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-12, January.
    • Handle: RePEc:hin:jijmms:912857
    DOI: 10.1155/S0161171203013097
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