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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2002 • Question 9

Question

Math 6310 • Algebra Fall 2002 • Question 9

Let \(E\) be a finite separable extension of a field \(K\) and let \(F\) be any finite field extension of \(K\). Show that \(E\otimes _K F\) is a finite product of fields.

Raw LaTeX

Let \(E\) be a finite separable extension of a field \(K\) and let \(F\) be any finite field extension
of \(K\). Show that \(E\otimes_K F\) is a finite product of fields.

Topic Tags

Field Extensions Finite Fields Irreducible Polynomials Tensor Products of Modules