On the lattice of fuzzy ideals of a ring

First, we prove that mu boolean OR eta = mu + eta in the lattice of all fuz zy (left, right) ideals with the same tip "t" using the technique of strong cut. By this we obtain the following results: (1) We point out that the la ttice of all fuzzy ideals of a ring is not distributive, thus the main theo rem (L-F1(R) is distributive) in Majumdar and Sultana (1996) is erroneous. (2) The lattice of all fuzzy (left, right) ideals with same tip "t", of a r ing R is modular, this generalizes the main theorem in Ajmal and Thomas (19 95). (C) 2000 Elsevier Science B.V. All rights reserved.