8. Derive the following results: a) The identity element of a subfield is the same as that of the field. b) If (F., +,) is an indexed collection of subfields of the field (F,+, ), then (n Fi, 4,) is also a subfield of (F, +,).

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.2: Divisibility And Greatest Common Divisor
Problem 33E
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8. Derive the following results:
a) The identity element of a subfield is the same as that of the field.
b) If (F., +, ) is an indexed collection of subfields of the field (F,+.), then
(n Pi, t,) is also a subfield of (F,-+, ).
Transcribed Image Text:8. Derive the following results: a) The identity element of a subfield is the same as that of the field. b) If (F., +, ) is an indexed collection of subfields of the field (F,+.), then (n Pi, t,) is also a subfield of (F,-+, ).
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