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Primeness and semiprimeness in posets. (English) Zbl 1212.06001

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.

MSC:

06A06 Partial orders, general
06A11 Algebraic aspects of posets