EUDML | On prime and principal ideals on graphs

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Displaying similar documents to “On prime and principal ideals on graphs”

On prime ideals of $C (X)$

Attilio Le Donne (1977)

Rendiconti del Seminario Matematico della Università di Padova

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Primary factorization in semigroups

E. W. Johnson (1986)

Czechoslovak Mathematical Journal

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Prime and maximal ideals of partially ordered sets

Marcel Erné (2006)

Mathematica Slovaca

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Primeness and semiprimeness in posets

Vilas S. Kharat, Khalid A. Mokbel (2009)

Mathematica Bohemica

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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.