Displaying similar documents to “Characterizations of the 0 -distributive semilattice”

Prime ideals in 0-distributive posets

Vinayak Joshi, Nilesh Mundlik (2013)

Open Mathematics

Similarity:

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

Similarity:

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...

Ideals in distributive posets

Cyndyma Batueva, Marina Semenova (2011)

Open Mathematics

Similarity:

We prove that any ideal in a distributive (relative to a certain completion) poset is an intersection of prime ideals. Besides that, we give a characterization of n-normal meet semilattices with zero, thus generalizing a known result for lattices with zero.