An Extension of M. C. R. Butler’s Theorem on Endomorphism Rings

Manfred Dugas; Daniel Herden; Saharon Shelah

doi:10.1007/978-3-319-51718-6_13

An Extension of M. C. R. Butler’s Theorem on Endomorphism Rings

Manfred Dugas^*
, Daniel Herden
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

We will prove the following theorem: Let D be the ring of algebraic integers of a finite Galois field extension F of 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.

Original language	English
Title of host publication	Coresource 4
Publisher	Springer International Publishing
Pages	277-284
Number of pages	8
ISBN (Electronic)	9783319517186
ISBN (Print)	9783319517179
DOIs	https://doi.org/10.1007/978-3-319-51718-6_13
State	Published - 2017

Bibliographical note

Publisher Copyright:
Springer International Publishing AG 2017.

Keywords

Butler’s theorem
Endomorphism rings

Access to Document

10.1007/978-3-319-51718-6_13

Cite this

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AU - Shelah, Saharon

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N2 - We will prove the following theorem: Let D be the ring of algebraic integers of a finite Galois field extension F of 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.

AB - We will prove the following theorem: Let D be the ring of algebraic integers of a finite Galois field extension F of 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.

KW - Butler’s theorem

KW - Endomorphism rings

UR - https://www.scopus.com/pages/publications/105032272286

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An Extension of M. C. R. Butler’s Theorem on Endomorphism Rings

Abstract

Bibliographical note

Keywords

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