# 0-distributive posets

Khalid A. Mokbel; Vilas S. Kharat

Mathematica Bohemica (2013)

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

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topA. 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 -

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