On lattice of basic z-ideals
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Abstract:
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.
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Journal title
volume 7 issue None
pages 0- 0
publication date 2021-05
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