On prime ideals of
Attilio Le Donne (1977)
Rendiconti del Seminario Matematico della Università di Padova
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Primeness and semiprimeness in posets
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The concept of a semiprime ideal in a poset is introduced. Characterizations of semiprime ideals in a poset as well as characterizations of a semiprime ideal to be prime in are obtained in terms of meet-irreducible elements of the lattice of ideals of and in terms of maximality of ideals. Also, prime ideals in a poset are characterized.