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On n-normal posets

100%
Halaš R., Joshi V., Kharat V.
Open Mathematics
|
2010
|
tom 8
|
nr 5
985-991
EN
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.
2
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Ideals in distributive posets

86%
Batueva C., Semenova M.
Open Mathematics
|
2011
|
tom 9
|
nr 6
1380-1388
EN
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.
3
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Prime ideals in 0-distributive posets

86%
Joshi V., Mundlik N.
Open Mathematics
|
2013
|
tom 11
|
nr 5
940-955
EN
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 with the generalization of the classical theorem of Nachbin. In fact, we prove that a dually atomic pseudocomplemented, 1-distributive poset is complemented if and only if the poset of prime ideals is unordered. In the last section, we have characterized 0-distributive posets by means of prime ideals and minimal prime ideals.
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