An introduction to the algebra of rings and fields
Fuente:
arXiv
Guardado en:
| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908493289619456 |
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| author | Grinberg, Darij |
| author_facet | Grinberg, Darij |
| contents | This is an introduction to rings and fields, written for a quarter-long undergraduate course. It includes the basic properties of ideals, modules, algebras and polynomials, the constructions of ring extensions and finite fields, some number-theoretical applications (such as a proof of quadratic reciprocity and Jacobsthal's formulas for $p = x^2 + y^2$), and tastes of Gröbner bases and the Smith normal form. Familiarity with groups and vector spaces is assumed, though no deep results from either theory are used.
Over 200 exercises are included (mostly without solutions). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13165 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An introduction to the algebra of rings and fields Grinberg, Darij Rings and Algebras Number Theory 16-01, 13-01, 12-01, 12E20, 11Axx This is an introduction to rings and fields, written for a quarter-long undergraduate course. It includes the basic properties of ideals, modules, algebras and polynomials, the constructions of ring extensions and finite fields, some number-theoretical applications (such as a proof of quadratic reciprocity and Jacobsthal's formulas for $p = x^2 + y^2$), and tastes of Gröbner bases and the Smith normal form. Familiarity with groups and vector spaces is assumed, though no deep results from either theory are used. Over 200 exercises are included (mostly without solutions). |
| title | An introduction to the algebra of rings and fields |
| topic | Rings and Algebras Number Theory 16-01, 13-01, 12-01, 12E20, 11Axx |
| url | https://arxiv.org/abs/2508.13165 |