Prime ideals in 0-distributive posets

Vinayak Joshi; Nilesh Mundlik

Displaying similar documents to “Prime ideals in 0-distributive posets”

0-distributive posets

Khalid A. Mokbel, Vilas S. Kharat (2013)

Mathematica Bohemica

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Several characterizations of 0-distributive posets are obtained by using the prime ideals as well as the semiprime ideals. It is also proved that if every proper $l$ -filter of a poset is contained in a proper semiprime filter, then it is $0$ -distributive. Further, the concept of a semiatom in 0-distributive posets is introduced and characterized in terms of dual atoms and also in terms of maximal annihilator. Moreover, semiatomic 0-distributive posets are defined and characterized. It is...

Prime and maximal ideals of partially ordered sets

Marcel Erné (2006)

Mathematica Slovaca

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Annihilators and ideals in ordered sets

Radomír Halaš (1995)

Czechoslovak Mathematical Journal

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On n-normal posets

Radomír Halaš, Vinayak Joshi, Vilas Kharat (2010)

Open Mathematics

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A poset Q is called n-normal, if its every prime ideal contains at most n minimal prime ideals. In this paper, using the prime ideal theorem for finite ideal distributive posets, some properties and characterizations of n-normal posets are obtained.

Primeness and semiprimeness in posets

Vilas S. Kharat, Khalid A. Mokbel (2009)

Mathematica Bohemica

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The concept of a semiprime ideal in a poset is introduced. Characterizations of semiprime ideals in a poset $P$ as well as characterizations of a semiprime ideal to be prime in $P$ are obtained in terms of meet-irreducible elements of the lattice of ideals of $P$ and in terms of maximality of ideals. Also, prime ideals in a poset are characterized.