The smallest number of free closed filters
Jan Pelant, Petr Simon, Jerry Vaughan (1988)
Fundamenta Mathematicae
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Jan Pelant, Petr Simon, Jerry Vaughan (1988)
Fundamenta Mathematicae
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Zdeněk Frolík (1972)
Commentationes Mathematicae Universitatis Carolinae
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Jerison, M.
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John W. Carlson (1980)
Commentationes Mathematicae Universitatis Carolinae
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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...