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کاربرد نوع شرط:
- جایگاه : پژوهشی
- مجله: Categories and General Algebraic Structures with Applications
- نوع مقاله: Journal Article
- کلمات کلیدی: Minimal ideal,Socle,real-valued functions ring,ring with property $(A)$
- چکیده:
- چکیده انگلیسی: 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).
- انتشار مقاله: 22-09-1395
- نویسندگان: Ali Asghar Estaji,Ebrahim Hashemi,Ali Akbar Estaji
- مشاهده