ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 03E72, 13A15 Murali, V., Rhodes University, Grahamstown, South Africa On Krull Intersection Theorem of Fuzzy Ideals A fuzzy ideal of a commutative ring R is a mapping μ : R → I, the unit interval with the usual ordering, satisfying μ(r−s) ≥ μ(r)∧μ(s) and μ(rs) ≥

μ(r) ∨ μ(s). For 0 < λ ≤ 1, r^{λ} is a fuzzy point if r^{λ}(s) = \{ \begin{matrix}λ & if s = r \\ 0 & if s ≠ r \end{matrix}

First we extend the notions of prime ideal, primary and radical of a fuzzy ideal, using fuzzy points. Secondly we characterise a primary decomposition of a fuzzy ideal. We give some applications to Nakayama’s Lemma and Krull Intersection Theorem. This is a joint work with B. B. Makamba of University of Fort Hare, Alice, South Africa. Reference: D. S. Malik and J. N. Mordeson, Fuzzy primary representations of fuzzy ideals. Inf. Sci. 55 (1991), 151 -165