A generalized Dumas irreducibility criterion
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917106573901824 |
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| author | Garg, Rishu Singh, Jitender |
| author_facet | Garg, Rishu Singh, Jitender |
| contents | As an extension of the classical irreducibility result of Dumas, a factorization result for polynomials over any valued field with a Krull valuation of arbitrary rank is proved. Further, a lower degree factor bound on factors of a given polynomial over a valued field with a Krull valuation is proved. These factorization results not only unify several known irreducibility results for polynomials over the said domains but also provide us sharp bounds on degrees of irreducible factors of the underlying polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21427 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A generalized Dumas irreducibility criterion Garg, Rishu Singh, Jitender Number Theory Commutative Algebra Algebraic Geometry 12E05, 11C08 As an extension of the classical irreducibility result of Dumas, a factorization result for polynomials over any valued field with a Krull valuation of arbitrary rank is proved. Further, a lower degree factor bound on factors of a given polynomial over a valued field with a Krull valuation is proved. These factorization results not only unify several known irreducibility results for polynomials over the said domains but also provide us sharp bounds on degrees of irreducible factors of the underlying polynomials. |
| title | A generalized Dumas irreducibility criterion |
| topic | Number Theory Commutative Algebra Algebraic Geometry 12E05, 11C08 |
| url | https://arxiv.org/abs/2511.21427 |