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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2009 • Question 9

Question

Math 6310 • Algebra Spring 2009 • Question 9

Let \(K\) be a subfield of a field \(L\). If \(\sigma :L\longrightarrow L\) is a homomorphism that fixes all elements of \(K\), is \(\sigma \) necessarily an automorphism of \(L\)? Justify your answer.

Raw LaTeX

Let \(K\) be a subfield of a field \(L\). If \(\sigma:L\longrightarrow L\) is a homomorphism that
fixes all elements of \(K\), is \(\sigma\) necessarily an automorphism of \(L\)? Justify your answer.

Topic Tags

Field Extensions Hom Functors and Module Homomorphisms Polynomial Rings and Ring Homomorphism Kernels