M. Sambasiva Rao (2012)
Archivum Mathematicum
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The concept of -ideals is introduced in a pseudo-complemented distributive lattice and some properties of these ideals are studied. Stone lattices are characterized in terms of -ideals. A set of equivalent conditions is obtained to characterize a Boolean algebra in terms of -ideals. Finally, some properties of -ideals are studied with respect to homomorphisms and filter congruences.
Bordalo, G. (1980)
Portugaliae mathematica
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Martin Goldstern, Miroslav Ploščica (2002)
Discussiones Mathematicae - General Algebra and Applications
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We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.
František Fiala (1970)
Archivum Mathematicum
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Ladislav Beran (1995)
Collectanea Mathematica
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Radomír Halaš (1995)
Czechoslovak Mathematical Journal
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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...