STRONGLY IRREDUCIBLE IDEALS

Abstract

AbstractA proper ideal I of a ring R is said to be strongly irreducible if for each pair of ideals A and B of R, $A\cap B \subseteq I$ implies that either $A \subseteq I$ or $B \subseteq I$. In this paper we study strongly irreducible ideals in different rings. The relations between strongly irreducible ideals of a ring and strongly irreducible ideals of localizations of the ring are also studied. Furthermore, a topology similar to the Zariski topology related to strongly irreducible ideals is introduced. This topology has the Zariski topology defined by prime ideals as one of its subspace topologies.