Fuzzy ideals of artinian rings

Abstract

The object of this paper is to study fuzzy ideals over Artinian rings. Among others we prove that a ring with unity is left (right) Artinian if and only if every fuzzy left (right) ideal μ of R is finite valued. This gives a characterization of artinian rings in terms of fuzzy ideals. Mukherjee and Sen (1987) proved that if every fuzzy ideal of a ring with unity is finite valued then the ring is Noetherian. We give an example to show that the converse of this theorem is not true. We also show that certain results of Pan (1987) are not true. © 1990.