On Property (A) and the socle of the $f$-ring $Frm(mathcal{P}(mathbb R), L)$

ali asghar Estaji, Ebrahim Hashemi, ali akbar Estaji
2018 Categories and General Algebraic Structures with Applications  
For a frame L, consider the f -ring FP L = F rm(P(R), L). In this paper, first we show that each minimal ideal of FP L 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 FP L consists of those f for which coz(f ) is a join of finitely many atoms. Also it is shown that not only FP L has Property (A) but also if L has a finite number of atoms then the residue class ring FP L/Soc(FP L) has Property (A).
doi:10.29252/cgasa.8.1.61 fatcat:jza7b6i3pfdd7dhmhpqoew2cvi