Vilas S. Kharat, Department of Mathematics, University of Pune, Pune 411 007, India, e-mail: vsk@math.unipune.ernet.in, khalidalaghbari@yahoo.com
Abstract: 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.
Keywords: semiprime ideal, prime ideal, meet-irreducible element, $I$-atom
Classification (MSC 2000): 06B10
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