Abstract
It is not always desirable to deal only with field extensions. Sometimes one wants to obtain a field extension by reducing a ring extension modulo a prime ideal. This procedure occurs in several contexts, and so we are led to give the basic theory of Galois automorphisms over rings, looking especially at how the Galois automorphisms operate on prime ideals or the residue class fields. The two examples given after Theorem 2.9 show the importance of working over rings, to get families of extensions in two very different contexts.
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© 2002 Springer Science+Business Media New York
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Lang, S. (2002). Extensions of Rings. In: Algebra. Graduate Texts in Mathematics, vol 211. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0041-0_7
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DOI: https://doi.org/10.1007/978-1-4613-0041-0_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6551-1
Online ISBN: 978-1-4613-0041-0
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