فهرست نشریات علمی دسترسی آزاد ایران

We show that the lattice of all ideals of a ring $R$ can be embedded in the lattice of all its fuzzyideals in uncountably many ways. For this purpose, we introduce the concept of the generalizedcharacteristic function $\chi _{s}^{r} (A)$ of a subset $A$ of a ring $R$ forfixed $r , s\in [0,1] $ and show that $A$ is an ideal of $R$ if, and only if, its generalizedcharacteristic function $\chi _{s}^{r} (A)$ is a fuzzy ideal of $R$. We alsoshow that the set of all generalized characteristic functions $C_{s}^{r}(I(R))$ of the members of $I(R)$ for fixed $r , s\in [0,1] $ is acomplete sublattice of the lattice of all fuzzy ideals of $R$ and establishthat this latter lattice is generated by the union of allits complete sublattices $C_{s}^{r} (I(R))$.