On prime and principal ideals on graphs

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.

Topological representations of distributive lattices and Brouwerian logics

Marshall Harvey Stone (1938)

Časopis pro pěstování matematiky a fysiky

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P-ideals and F-ideals in rings of continuous functions

David Rudd (1975)

Fundamenta Mathematicae

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