Strongly irreducible ring and its S spectrum - Ahmad, Hemin A.; Hummadi, Parween A. (Iraqi Journal of Science, 2024)
Let Κ be a proper ideal of a commutative ring S. Then Κ is a strongly irreducible (SI) ideal if for any two ideals C and D of S, C∩D⊆ Κ implies C ⊆ Κ or D ⊆ Κ. We say a ring is strongly irreducible (SI) if all its ideals are strongly irreducible. In this paper some properties of such ring are given. The relations between SI rings and some types of rings are also studied. Furthermore, for an SI ring S we study the S spectrum of S and the S.spec(S) topology.