Show that if \(\alpha \) and \(\beta \) are elements of a field \(E\) which are algebraic over a subfield \(F\), then \(\alpha +\beta \) and \(\alpha \beta \) are algebraic over \(F\).
Question
Math 6310 • Algebra
Fall 1999 • Question 5
Question
Fall 1999 • Question 5
Show that if \(\alpha \) and \(\beta \) are elements of a field \(E\) which are algebraic over a subfield \(F\), then \(\alpha +\beta \) and \(\alpha \beta \) are algebraic over \(F\).