When every finitely generated ideal is S-principal
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929332419559424 |
|---|---|
| author | Chhiti, Mohamed Mahdou, Salah Eddine Moutui, Moutu Abdou Salam |
| author_facet | Chhiti, Mohamed Mahdou, Salah Eddine Moutui, Moutu Abdou Salam |
| contents | In this paper, we introduce the concept of $S$-Bézout ring, as a generalization of Bézout ring. We investigate the relationships between $S$-Bézout and other related classes of rings. We establish some characterizations of $S$-Bézout rings. We study this property in various contexts of commutative rings including direct product, localization, trivial ring extensions and amalgamation rings. Our results allow us to construct new original classes of $S$-Bézout rings subject to various ring theoretical properties. Furthermore, we introduce the notion of nonnil $S$-Bézout ring and establish some characterizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_07373 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | When every finitely generated ideal is S-principal Chhiti, Mohamed Mahdou, Salah Eddine Moutui, Moutu Abdou Salam Commutative Algebra 13A15, 13B99, 13E15 I.2.8 In this paper, we introduce the concept of $S$-Bézout ring, as a generalization of Bézout ring. We investigate the relationships between $S$-Bézout and other related classes of rings. We establish some characterizations of $S$-Bézout rings. We study this property in various contexts of commutative rings including direct product, localization, trivial ring extensions and amalgamation rings. Our results allow us to construct new original classes of $S$-Bézout rings subject to various ring theoretical properties. Furthermore, we introduce the notion of nonnil $S$-Bézout ring and establish some characterizations. |
| title | When every finitely generated ideal is S-principal |
| topic | Commutative Algebra 13A15, 13B99, 13E15 I.2.8 |
| url | https://arxiv.org/abs/2301.07373 |