A constructive proof of Orzech's theorem

Darij Grinberg

doi:10.48550/arxiv.2604.13911

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A constructive proof of Orzech's theorem

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A constructive proof of Orzech's theorem

Darij Grinberg

ArXiv.org

15 Apr 2026

DOI: https://doi.org/10.48550/arxiv.2604.13911

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Abstract

Mathematics - Commutative Algebra

Mathematics - Rings and Algebras

LetAbe a commutative ring with unity, andMa finitely generatedA -module. In 1971, Morris Orzech showed that anyA -module homomorphism from a submodule ofMtoMmust be an isomorphism. We give a constructive proof of this fact using the Cayley–Hamilton theorem.

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Title: A constructive proof of Orzech's theorem
Creators: Darij Grinberg - Drexel University
Publication Details: ArXiv.org
Resource Type: Preprint
Language: English
Academic Unit: Mathematics
Other Identifier: 991022173526604721

A constructive proof of Orzech's theorem

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Abstract

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