0-distributive posets

Khalid A. Mokbel; Vilas S. Kharat

Mathematica Bohemica (2013)

  • Volume: 138, Issue: 3, page 325-335
  • ISSN: 0862-7959

Abstract

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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 shown that a 0 -distributive poset P is semiatomic if and only if the intersection of all non dense prime ideals of P equals ( 0 ] . Some counterexamples are also given.

How to cite

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A. Mokbel, Khalid, and S. Kharat, Vilas. "0-distributive posets." Mathematica Bohemica 138.3 (2013): 325-335. <http://eudml.org/doc/260577>.

@article{A2013,
abstract = {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 shown that a $0$-distributive poset $P$ is semiatomic if and only if the intersection of all non dense prime ideals of $P$ equals $(0]$. Some counterexamples are also given.},
author = {A. Mokbel, Khalid, S. Kharat, Vilas},
journal = {Mathematica Bohemica},
keywords = {0-distributive poset; ideal; semiprime ideal; prime ideal; semiatom; semiatomic 0-distributive poset; 0-distributive poset; prime ideal; semiprime ideal; semi-atom; semi-atomic poset},
language = {eng},
number = {3},
pages = {325-335},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {0-distributive posets},
url = {http://eudml.org/doc/260577},
volume = {138},
year = {2013},
}

TY - JOUR
AU - A. Mokbel, Khalid
AU - S. Kharat, Vilas
TI - 0-distributive posets
JO - Mathematica Bohemica
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 138
IS - 3
SP - 325
EP - 335
AB - 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 shown that a $0$-distributive poset $P$ is semiatomic if and only if the intersection of all non dense prime ideals of $P$ equals $(0]$. Some counterexamples are also given.
LA - eng
KW - 0-distributive poset; ideal; semiprime ideal; prime ideal; semiatom; semiatomic 0-distributive poset; 0-distributive poset; prime ideal; semiprime ideal; semi-atom; semi-atomic poset
UR - http://eudml.org/doc/260577
ER -

References

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