Prime ideals in 0-distributive posets

• Autorzy: Vinayak Joshi , Nilesh Mundlik
• Języki publikacji: 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.

Słowa kluczowe

EN

0-distributive poset; Prime ideal; Minimal prime ideal; Dense ideal; Maximal l-filter; Pseudocomplemented poset

Kategorie tematyczne

• 06B10: Ideals, congruence relations
• 06A12: Semilattices

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 5
• Strony: 940-955

Daty

wydano

2013-05-01

online

2013-03-14

Twórcy

autor

Vinayak Joshi

• University of Pune

autor

Nilesh Mundlik

• Nowrosjee Wadia College of Arts and Science

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Identyfikatory

DOI

10.2478/s11533-013-0206-z