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Power-ordered sets

Martin R. Goldstern, Dietmar Schweigert (2002)

Discussiones Mathematicae - General Algebra and Applications

We define a natural ordering on the power set 𝔓(Q) of any finite partial order Q, and we characterize those partial orders Q for which 𝔓(Q) is a distributive lattice under that ordering.

Prime ideals in 0-distributive posets

Vinayak Joshi, Nilesh Mundlik (2013)

Open Mathematics

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 generalization...

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