TY - JOUR T1 - On lattice of Basic Z-Ideals TT - شبکۀ z-ایده‌آل‌های پایه‌ای JF - khu-mmr JO - khu-mmr VL - 7 IS - 1 UR - http://mmr.khu.ac.ir/article-1-2961-en.html Y1 - 2021 SP - 127 EP - 132 KW - F-ring KW - lattice KW - Zariski topology KW - Semiprimitive ring KW - Reduced ring. N2 - For an f-ring with bounded inversion property, we show that , the set of all basic z-ideals of , partially ordered by inclusion is a bounded distributive lattice. Also, whenever is a semiprimitive ring, , the set of all basic -ideals of , partially ordered by inclusion is a bounded distributive lattice. Next, for an f-ring with bounded inversion property, we prove that is a complemented lattice and is a semiprimitive ring if and only if is a complemented lattice and is a reduced ring if and only if the base elements for closed sets in the space are open and is semiprimitive if and only if the base elements for closed sets in the space are open and is reduced. As a result, whenever (i.e., the ring of continuous functions), we have is a complemented lattice if and only if is a complemented lattice if and only if is a -space../files/site1/files/71/12.pdf M3 10.52547/mmr.7.1.127 ER -