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Semidistributivity, prime ideals and the subbase lemma

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

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  • Marcel Erné

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OriginalspracheEnglisch
Seiten (von - bis)241-250
Seitenumfang10
FachzeitschriftRendiconti del Circolo Matematico di Palermo
Jahrgang41
Ausgabenummer2
PublikationsstatusVeröffentlicht - Mai 1992

Abstract

We generalize the notions of semidistributive elements and of prime ideals from lattices to arbitrary posets. Then we show that the Boolean prime ideal theorem is equivalent to the statement that if a poset P has a join-semidistributive top element then each proper ideal of P is contained in a prime ideal, while the converse implication holds without any choice principle. Furthermore, the prime ideal theorem is shown to be equivalent to the following order-theoretical generalization of Alexander's subbase lemma: If the top element of a poset P is join-semidistributive and compact in some subbase of P then it is compact in P.

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Semidistributivity, prime ideals and the subbase lemma. / Erné, Marcel.
in: Rendiconti del Circolo Matematico di Palermo, Jahrgang 41, Nr. 2, 05.1992, S. 241-250.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Erné, M 1992, 'Semidistributivity, prime ideals and the subbase lemma', Rendiconti del Circolo Matematico di Palermo, Jg. 41, Nr. 2, S. 241-250. https://doi.org/10.1007/BF02844668
Erné, M. (1992). Semidistributivity, prime ideals and the subbase lemma. Rendiconti del Circolo Matematico di Palermo, 41(2), 241-250. https://doi.org/10.1007/BF02844668
Erné M. Semidistributivity, prime ideals and the subbase lemma. Rendiconti del Circolo Matematico di Palermo. 1992 Mai;41(2):241-250. doi: 10.1007/BF02844668
Erné, Marcel. / Semidistributivity, prime ideals and the subbase lemma. in: Rendiconti del Circolo Matematico di Palermo. 1992 ; Jahrgang 41, Nr. 2. S. 241-250.
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