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2013 | 11 | 5 | 940-955
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Prime ideals in 0-distributive posets

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EN
Abstrakty
EN
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 of the classical theorem of Nachbin. In fact, we prove that a dually atomic pseudocomplemented, 1-distributive poset is complemented if and only if the poset of prime ideals is unordered. In the last section, we have characterized 0-distributive posets by means of prime ideals and minimal prime ideals.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
5
Strony
940-955
Opis fizyczny
Daty
wydano
2013-05-01
online
2013-03-14
Twórcy
Bibliografia
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0206-z
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