Displaying similar documents to “Primeness and semiprimeness in posets”

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.

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...

Ideals in distributive posets

Cyndyma Batueva, Marina Semenova (2011)

Open Mathematics

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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.