Prime ideals in 0-distributive posets

@article{Joshi2013PrimeII,
  title={Prime ideals in 0-distributive posets},
  author={V. Joshi and Nilesh Mundlik},
  journal={Central European Journal of Mathematics},
  year={2013},
  volume={11},
  pages={940-955}
}
In the first section of this paper, we prove an analogue of Stone’s Theorem for posets satisfying DCC by using semiprime ideals. We also prove the existence of prime ideals in atomic posets in which atoms are dually distributive. Further, it is proved that every maximal non-dense (non-principal) ideal of a 0-distributive poset (meet-semilattice) is prime. The second section focuses on the characterizations of (minimal) prime ideals in pseudocomplemented posets. The third section deals with the… Expand

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References

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Pseudo-complements in posets
Semiprime Ideals and Separation Theorems for Posets
Semiprime ideals in general lattices
Ideals in distributive posets
Standard completions for quasiordered sets
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