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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.
Hashemi et al. (Tue,) studied this question.
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