A generalization of strongly irreducible ideals with a view towards rings of continuous functions
Submitted: 2024-02-27
|Accepted: 2024-05-09
|Published: 2024-10-01
Copyright (c) 2024 Jamal Hashemi, Hossein Yari
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
pseudoprime ideal, strongly irreducible ideal, semi-strongly irreducible ideal, rings of continuous functions
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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.
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