Displaying similar documents to “0-distributive posets”

Prime ideals in 0-distributive posets

Vinayak Joshi, Nilesh Mundlik (2013)

Open Mathematics

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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...

Characterizations of the 0 -distributive semilattice

P. Balasubramani (2003)

Mathematica Bohemica

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The 0 -distributive semilattice is characterized in terms of semiideals, ideals and filters. Some sufficient conditions and some necessary conditions for 0 -distributivity are obtained. Counterexamples are given to prove that certain conditions are not necessary and certain conditions are not sufficient.