فهرست نشریات علمی دسترسی آزاد ایران

For a frame $L$, consider the $f$-ring $ \mathcal{F}_{\mathcal P}L=Frm(\mathcal{P}(\mathbb R), L)$. In this paper, first we show that each minimal ideal of $ \mathcal{F}_{\mathcal P}L$ is a principal ideal generated by $f_a$, where $a$ is an atom of $L$. Then we show that if $L$ is an $\mathcal{F}_{\mathcal P}$-completely regular frame, then the socle of $ \mathcal{F}_{\mathcal P}L$ consists of those $f$ for which $coz (f)$ is a join of finitely many atoms.  Also it is shown that not only $ \mathcal{F}_{\mathcal P}L$ has Property (A) but also if $L$ has a finite number of atoms then the residue class ring $ \mathcal{F}_{\mathcal P}L/\mathrm{Soc}( \mathcal{F}_{\mathcal P}L)$ has Property (A).