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

[EN] In this article, 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.