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This preview shows page 1 - 3 out of 9 pages. Subscribe to view the full document. I cannot even describe how much Course Hero helped me this summer. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

University of Oslo. MAT Uploaded By augusthrocks. A fact that makes life easy working with fields, is that ring homomorphism between fields always are injective. And if in addition the two fields are of the same finite dimension over some ground field K and the homomorphism is an embedding over K that is, it is K -linear Fto bgil cewk negro gmuk telanjang, the homomorphism is also surjective.

Then Emb K L, L is a group. Indeed the composition of two embeddings over K is an embedding and this gives Emb K L, L a monoid structure. This group is the famous Galois group of L over K. In the more general case when L not necessarily is a finite extension, Emb K L, L is not always a group, but the subset of invertible embeddings is a group.

And in this case, this is the Galois group. Problem 1. X Problem 2. Let K be any field and let a 2 K be an element. When is f x irreducible? It is an extension of K. So E f comes equipped with a preferred root of f x. The degree of E f over K equals the degree n of fand the powers 1x. Indeed, sending x to! Hence we get a map E f! Share this link with a friend: Copied! Other Related Materials 10 pages. Ask Expert Tutors You can ask bonus questions You can ask questions expire soon You can ask Fto bgil cewk negro gmuk telanjang will expire.

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