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 ⊆...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/210346 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/210346 |
| Access Level: | acceso abierto |
| Palabra clave: | Pseudoprime ideal Strongly irreducible ideal Semi-strongly irreducible ideal Rings of continuous functions |
| Sumario: | [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. |
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