Displaying similar documents to “On prime ideals of C ( X )

Prime ideals in 0-distributive posets

Vinayak Joshi, Nilesh Mundlik (2013)

Open Mathematics

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In the first section of this paper, we prove an analogue of Stone’s Theorem for posets satisfying DCC by using semiprime ideals. We also prove the existence of prime ideals in atomic posets in which atoms are dually distributive. Further, it is proved that every maximal non-dense (non-principal) ideal of a 0-distributive poset (meet-semilattice) is prime. The second section focuses on the characterizations of (minimal) prime ideals in pseudocomplemented posets. The third section deals...

Star-invertible ideals of integral domains

Gyu Whan Chang, Jeanam Park (2003)

Bollettino dell'Unione Matematica Italiana

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Let be a star-operation on R and s the finite character star-operation induced by . The purpose of this paper is to study when = v or s = t . In particular, we prove that if every prime ideal of R is -invertible, then = v , and that if R is a unique -factorable domain, then R is a Krull domain.