A constructive proof of Orzech's theorem
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | |
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| _version_ | 1866911600449945600 |
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| author | Grinberg, Darij |
| author_facet | Grinberg, Darij |
| contents | Let $A$ be a commutative ring with unity, and $M$ a finitely generated $A$-module. In 1971, Morris Orzech showed that any surjective $A$-module homomorphism from a submodule of $M$ to $M$ must be an isomorphism. We give a constructive proof of this fact using the Cayley--Hamilton theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13911 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A constructive proof of Orzech's theorem Grinberg, Darij Commutative Algebra Rings and Algebras 13C10, 15A15 Let $A$ be a commutative ring with unity, and $M$ a finitely generated $A$-module. In 1971, Morris Orzech showed that any surjective $A$-module homomorphism from a submodule of $M$ to $M$ must be an isomorphism. We give a constructive proof of this fact using the Cayley--Hamilton theorem. |
| title | A constructive proof of Orzech's theorem |
| topic | Commutative Algebra Rings and Algebras 13C10, 15A15 |
| url | https://arxiv.org/abs/2604.13911 |