Geodesic
Primeness and semiprimeness in posets
Mathematica Bohemica, Tome 134 (2009) no. 1, pp. 19-30

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
The concept of a semiprime ideal in a poset is introduced. Characterizations of semiprime ideals in a poset $P$ as well as characterizations of a semiprime ideal to be prime in $P$ are obtained in terms of meet-irreducible elements of the lattice of ideals of $P$ and in terms of maximality of ideals. Also, prime ideals in a poset are characterized.
The concept of a semiprime ideal in a poset is introduced. Characterizations of semiprime ideals in a poset $P$ as well as characterizations of a semiprime ideal to be prime in $P$ are obtained in terms of meet-irreducible elements of the lattice of ideals of $P$ and in terms of maximality of ideals. Also, prime ideals in a poset are characterized.
DOI : 10.21136/MB.2009.140636
Classification : 06B10
Keywords: semiprime ideal; prime ideal; meet-irreducible element; $I$-atom 
Kharat, Vilas S.; Mokbel, Khalid A. Primeness and semiprimeness in posets. Mathematica Bohemica, Tome 134 (2009) no. 1, pp. 19-30. doi: 10.21136/MB.2009.140636
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