شماره ركورد كنفرانس :
3735
عنوان مقاله :
A short note on compact frames
پديدآورندگان :
Abedi Mostafa abedi@esfarayen.ac.ir Esfarayen University of Technology
كليدواژه :
Compact frame , strongly fixed ideal , zero sets in pointfree topology
عنوان كنفرانس :
اولين كنفرانس منطقه اي علوم رياضي و كاربردها
چكيده فارسي :
A frame $L$ is called weakly spatial if for every element $a$ in $L$ other than the top element there is a prime element $P$ in $L$ such that $a\leq p$.
For a weakly spatial frame $L$, we observe that $L$ is a compact frame if and only if its spectrum $\Sigma L$ is a compact space.
Let $\mathcal RL$ be the ring of real-valued continuous
functions on a frame $L$. Whenever $L$ is a weakly spatial frame,
we show that $L$ is a compact frame if and only if every maximal ideal in $\mathcal RL$ is strongly fixed.