Let F be a field. a. Show that the collection of matrices a L = { [ ª d]: ab € K} -b forms a field L with respect to the usual addition and multiplication of matrices if and only if X² + 10 has no solution in F. b. Show that I contains a field isomorphic to F. c. Construct a field with 9 elements,

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A: Let's consider that 1+a-1∈Qa then, it can be concluded that, Q1+a-1⊆Qa                  …1

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Q: Abstract Algebra. Please explain everything in detail.

A: To describe all the field automorphisms of the given field.

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A: This question from ring theory

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Q: Which of the following structures is a field? (Zg, +,x). An integral domain with 81 elements. The…

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Q: Let 2={1,2,3,4,5,6}. Construct the minimal field containing 1. 8={{1,2}, {3,4}}

A: This is a problem of measure theory.

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