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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1998 • Question 8

Question

Math 6310 • Algebra Fall 1998 • Question 8

Let \(K/k\) be a Galois extension with Galois group \(G\). Show that every 1-cycle on \(G\) with values in \(K^*\) is a 1-coboundary.

Raw LaTeX

Let \(K/k\) be a Galois extension with Galois group \(G\). Show that every 1-cycle on \(G\) with
values in \(K^*\) is a 1-coboundary.

Topic Tags

Ext Functors and Module Extensions Field Extensions Galois Theory