On Property (A) and the socle of the f-ring Frm(P(R),L)

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