305 -Homework set 3

This set is due February 25 at the beginning of lecture. Consult the syllabus for details on the homework policy.

1. Show directly that there is no field of 6 elements. (“Directly” means, among other things, that you cannot use the facts mentioned without proof at the end of lecture 4.3.)

2. Construct a field of size 8. Once you are done, verify that all its elements satisfy the equation x^8-x=0.

3. Solve exercises 36–38 from Chapter 4 of the book.

4. Is the set \{a+b\root 4\of 2 : a,b\in{\mathbb Q}\} a field with the usual +,\times,0,1?

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This entry was posted on Wednesday, February 18th, 2009 at 1:34 pm and is filed under 305: Abstract Algebra I. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

2 Responses to 305 -Homework set 3

  1. 305 -Syllabus « Teaching page says:
    February 18, 2009 at 1:46 pm

    […] Homework 3, due February 25, at the beginning of lecture. Possibly related posts: (automatically generated)Buffalostyle Forges OnThe Myth About HomeworkHomework battles and the biggest genius in the school, part I […]

    Reply
  2. 305 -Syllabus | A kind of library says:
    February 17, 2019 at 6:34 am

    […] Homework 3, due February 25, at the beginning of lecture. […]

    Reply

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