A generalization of strongly irreducible ideals with a view towards rings of continuous functions

Abstract

In this note, we introduce and study the concept of a semi-strongly irreducible ideal, a natural generalization of a strongly irreducible ideal. We say an ideal I of a commutative ring R is semi-strongly irreducible if for ideals J and K of R, the inclusion J ∩ K ⊆ I implies that either J2 ⊆ I or K2 ⊆ I . After some general results, the article focuses on semi-strongly irreducible ideals in rings of continuous functions.

Keywords

• pseudoprime ideal
• strongly irreducible ideal
• semi-strongly irreducible ideal
• rings of continuous functions