Displaying similar documents to “Quantification of topological concepts using ideals.”

Primeness and semiprimeness in posets

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

Mathematica Bohemica

Similarity:

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.

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...