Kharat, Vilas S.; Mokbel, Khalid A. Primeness and semiprimeness in posets. (English) Zbl 1212.06001 Math. Bohem. 134, No. 1, 19-30 (2009). Summary: 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. Cited in 7 Documents MSC: 06A06 Partial orders, general 06A11 Algebraic aspects of posets Keywords:semiprime ideal; prime ideal; meet-irreducible element; \(I\)-atom × Cite Format Result Cite Review PDF Full Text: DOI EuDML