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A Field Extension as a Vector Space

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Field Theory

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 158))

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Abstract

In this chapter, we take a closer look at a finite field extension F < E from the point of view that E is a vector space over F. It is clear, for instance, that any σG F(E) is a linear operator on E over F. However, there are many linear operators that are not field automorphisms. One of the most important is multiplication by a fixed element of E, which we study next.

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© 1995 Steven Roman

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Roman, S. (1995). A Field Extension as a Vector Space. In: Field Theory. Graduate Texts in Mathematics, vol 158. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2516-4_8

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  • DOI: https://doi.org/10.1007/978-1-4612-2516-4_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94408-1

  • Online ISBN: 978-1-4612-2516-4

  • eBook Packages: Springer Book Archive

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