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Keywords:
semiprime ideal; prime ideal; meet-irreducible element; $I$-atom
semiprime ideal; prime ideal; meet-irreducible element; $I$-atom
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.
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