Not-so-fuzzy fuzzy ideals
The authors look for algebraic structures which do not admit proper fuzzy substructures. The main answer is the following: Theorem. If a ring R is Boolean, Artinian or a principal ideal domain, then in R any proper prime fuzzy ideal P has supp P\(=\{0\}\). As a generalization they get a characterization of rings with finite chains of ideals. Similar results were recently presented by \textit{D. S. Malik}, \textit{J. N. Mordeson} [Fuzzy Sets Syst. 37, 93-98 (1990; Zbl 0704.16002)] and \textit{D. S. Malik} [ibid. 37, 111-115 (1990; Zbl 0704.16017)].
scientific article; zbMATH DE number 4165093