Anyone willing to help me with my Modern Algebra questions?
Asked by
huey (
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)
March 9th, 2010
I have a take home quiz and need some help. Well this is the question: Prove that if F is a field, then it has exactly two ideals
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9 Answers
Sorry, but no homework questions here!
Sure. If it’s a question of “How do I… ?” and not “What is the answer to… ?”
Exactly, everyone here is willing to help you, but you have to ask a more specific question.
More specific = more answers.
More vague = fewer answers.
We don’t know what is on your quiz. Tell us. Then we might be able to help.
(x^2 – r^2) = (x + r) * (x – r)
42
You just asked a question about a question. That’s pretty circuitous.
What is your definition of “field” and “ideal” from your textbook? I only know how to solve algebra; it’s been a long time since I had to play with terms like this.
Clearly {0} is one ideal. Suppose that another ideal has a non-zero member r—since it’s a field, r must have a multiplicative inverse. If you understand the definition of an ideal, the proof should be obvious.
yes a field has only 2 ideals that r improper ideals.as a field is a commutative ring with unity so ideals are (0) and F itself.no proper ideals there.let I be the proper ideal .let x belongs to I .as F is a field therefore inverse of x belongs to field.then x*x-1 =1 belongs to I.if we take any elt from field Y.1*y =y belongs to ideal.therefore every elt of field belongs to ideal.then I=f.therefore only ideals r (0) and f itself
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