$\sigma$-Prime Spectrum of Almost Distributive Lattices
DOI:
https://doi.org/10.29020/nybg.ejpam.v17i2.5098Keywords:
almost distributive lattice (ADL), generalized Stone ADL, complemented ADL, relatively complemented ADL, normal ADL, minimal prime ideal, prime $\sigma$-ideal, prime $\alpha$-ideal, compact space, non-denseAbstract
For each $\alpha$-ideal of an almost distributive lattice (ADL) to become a $\sigma$-ideal, a set of equivalent conditions is derived, which tends to result in a characterization of generalized Stone ADLs. On an ADL, a one-to-one correspondence is derived between the set of all prime $\sigma$-ideals of the ADL and the set of all prime $\sigma$-ideals of the quotient ADL. Finally, proved some properties of prime $\sigma$-ideals of a normal ADL topologically.
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