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1. Suppose that E is an extension field of F, and a, bЄ E are algebraic over a field F, of degress m and n respectively. Show that if m and n have no common prime factor, then ab is algebraic over F. 2. What can you say about the degree of ab over F.

1. Suppose that E is an extension field of F, and a, bЄ E are algebraic over a field F, of degress m and n respectively. Show that if m and n have no common prime factor, then ab is algebraic over F. 2. What can you say about the degree of ab over F.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Suppose that E is an extension field of F, and a, bЄ E are algebraic over a field F, of degress m and n respectively. Show that if m and n have no common prime factor, then ab is algebraic over F. 2. What can you say about the degree of ab over F.
Transcribed Image Text:1. Suppose that E is an extension field of F, and a, bЄ E are algebraic over a field F, of degress m and n respectively. Show that if m and n have no common prime factor, then ab is algebraic over F. 2. What can you say about the degree of ab over F.
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