On prime ideals of
Attilio Le Donne (1977)
Rendiconti del Seminario Matematico della Università di Padova
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Attilio Le Donne (1977)
Rendiconti del Seminario Matematico della Università di Padova
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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...
Mark Mandelker (1968)
Fundamenta Mathematicae
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Giuliano Artico, Umberto Marconi (1976)
Rendiconti del Seminario Matematico della Università di Padova
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Ronnie Levy, Philippe Loustaunau, Jay Shapiro (1991)
Fundamenta Mathematicae
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Swapan Kumar Ghosh (2006)
Commentationes Mathematicae Universitatis Carolinae
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A space is called -compact by M. Mandelker if the intersection of all free maximal ideals of coincides with the ring of all functions in with compact support. In this paper we introduce -compact and -compact spaces and we show that a space is -compact if and only if it is both -compact and -compact. We also establish that every space admits a -compactification and a -compactification. Examples and counterexamples are given.