# Prime ideals in 0-distributive posets

Open Mathematics (2013)

- Volume: 11, Issue: 5, page 940-955
- ISSN: 2391-5455

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topVinayak Joshi, and Nilesh Mundlik. "Prime ideals in 0-distributive posets." Open Mathematics 11.5 (2013): 940-955. <http://eudml.org/doc/269405>.

@article{VinayakJoshi2013,

abstract = {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.},

author = {Vinayak Joshi, Nilesh Mundlik},

journal = {Open Mathematics},

keywords = {0-distributive poset; Prime ideal; Minimal prime ideal; Dense ideal; Maximal l-filter; Pseudocomplemented poset; prime ideal; minimal prime ideal; dense ideal; maximal 1-filter; pseudocomplemented poset},

language = {eng},

number = {5},

pages = {940-955},

title = {Prime ideals in 0-distributive posets},

url = {http://eudml.org/doc/269405},

volume = {11},

year = {2013},

}

TY - JOUR

AU - Vinayak Joshi

AU - Nilesh Mundlik

TI - Prime ideals in 0-distributive posets

JO - Open Mathematics

PY - 2013

VL - 11

IS - 5

SP - 940

EP - 955

AB - 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.

LA - eng

KW - 0-distributive poset; Prime ideal; Minimal prime ideal; Dense ideal; Maximal l-filter; Pseudocomplemented poset; prime ideal; minimal prime ideal; dense ideal; maximal 1-filter; pseudocomplemented poset

UR - http://eudml.org/doc/269405

ER -

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