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

• Hashemi, Jamal ^[1] ; Yari, Hossein ^[1]
  1. [1] Shahid Chamran University of Ahvaz

     Shahid Chamran University of Ahvaz

     Irán

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 25, Nº. 2, 2024, págs. 491-501
• Idioma: inglés
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• Resumen

  • 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.