Displaying similar documents to “Annihilators and ideals in ordered sets”

Prime ideals in 0-distributive posets

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...

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...

A characterization of finite Stone pseudocomplemented ordered sets

Radomír Halaš (1996)

Mathematica Bohemica

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A distributive pseudocomplemented set S [2] is called Stone if for all a ∈ S the condition L U ( a * , a * * ) = S holds. It is shown that in a finite case S is Stone iff the join of all distinct minimal prime ideals of S is equal to S .

Relative polars in ordered sets

Radomír Halaš (2000)

Czechoslovak Mathematical Journal

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In the paper, the notion of relative polarity in ordered sets is introduced and the lattices of R -polars are studied. Connections between R -polars and prime ideals, especially in distributive sets, are found.

Characterizations of the 0 -distributive semilattice

P. Balasubramani (2003)

Mathematica Bohemica

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The 0 -distributive semilattice is characterized in terms of semiideals, ideals and filters. Some sufficient conditions and some necessary conditions for 0 -distributivity are obtained. Counterexamples are given to prove that certain conditions are not necessary and certain conditions are not sufficient.