Abstract
We will prove the following theorem: Let D be the ring of algebraic integers of a finite Galois field extension F of \(\mathbb{Q}\) and E a D-algebra such that E is a locally free D-module of countable rank and all elements of E are algebraic over F. Then there exists a left D-submodule M ⊇ E of FE = E ⊗ D F such that the left multiplications by elements of E are the only D-linear endomorphisms of M.
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Acknowledgements
The third author was supported by European Research Council grant 338821. This is DgHeSh1091 in the third author’s list of publications.
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Dugas, M., Herden, D., Shelah, S. (2017). An Extension of M. C. R. Butler’s Theorem on Endomorphism Rings. In: Droste, M., Fuchs, L., Goldsmith, B., Strüngmann, L. (eds) Groups, Modules, and Model Theory - Surveys and Recent Developments . Springer, Cham. https://doi.org/10.1007/978-3-319-51718-6_13
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DOI: https://doi.org/10.1007/978-3-319-51718-6_13
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