Iterative Derivations on Central Simple Algebras
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914272394608640 |
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| author | Michel, Manujith K. Srinivasan, Varadharaj R. |
| author_facet | Michel, Manujith K. Srinivasan, Varadharaj R. |
| contents | We prove that an iterative derivation $δ_F$ on a field $F$ can be extended to an iterative derivation $δ_A$ on a central simple $F-$algebra $A$ if the characteristic of $F$ does not divide the exponent of $A$ in the Brauer group of $F.$ For a central simple $F-$algebra with an iterative derivation, we show the existence of a unique (up to isomorphism) Picard-Vessiot splitting field and from the nature its Galois group, we also describe the structure of the central simple algebra in terms of its $δ_A-$right ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15648 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Iterative Derivations on Central Simple Algebras Michel, Manujith K. Srinivasan, Varadharaj R. Rings and Algebras 12H05, 20Gxx We prove that an iterative derivation $δ_F$ on a field $F$ can be extended to an iterative derivation $δ_A$ on a central simple $F-$algebra $A$ if the characteristic of $F$ does not divide the exponent of $A$ in the Brauer group of $F.$ For a central simple $F-$algebra with an iterative derivation, we show the existence of a unique (up to isomorphism) Picard-Vessiot splitting field and from the nature its Galois group, we also describe the structure of the central simple algebra in terms of its $δ_A-$right ideals. |
| title | Iterative Derivations on Central Simple Algebras |
| topic | Rings and Algebras 12H05, 20Gxx |
| url | https://arxiv.org/abs/2601.15648 |