- #1
phillyj
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The class I'm in is not modern algebra nor have I take those courses. The professor of the class [Learning how to read/write in math] decided to try to teach some abstract algebra. I am trying to understand how multiplication is done in a field. I am using this site to help me as it was most relevant to making tables like the professor wanted:
http://math.arizona.edu/~ura-reports/041/Patterson.Genevieve/Final/FinalReport/node8.html
I am stuck on 9 element fields. This is the second to last example at the end of the page. I understand that we can extend the F[3] field to get the table.
The site says "As a vector space, F[9] = F[3^2] = {a+bx, (a,b)[tex]\in[/tex] F[3]}. To find the multiplication table we need a monic-quadratic that has no zeros in F[3]
A monic-quadratic will have a coefficient of 1 on the highest degree term."
[1]Why do they use monic quadratic?
[2] When they try x^2+1, they get f(0)=1, f(1)=2 but why is f(2)=2? Are they not plugging into x?
I don't really have good study material as the professor wrote a short paper on this stuff but it is bare minimum.
Thanks for your help.
http://math.arizona.edu/~ura-reports/041/Patterson.Genevieve/Final/FinalReport/node8.html
I am stuck on 9 element fields. This is the second to last example at the end of the page. I understand that we can extend the F[3] field to get the table.
The site says "As a vector space, F[9] = F[3^2] = {a+bx, (a,b)[tex]\in[/tex] F[3]}. To find the multiplication table we need a monic-quadratic that has no zeros in F[3]
A monic-quadratic will have a coefficient of 1 on the highest degree term."
[1]Why do they use monic quadratic?
[2] When they try x^2+1, they get f(0)=1, f(1)=2 but why is f(2)=2? Are they not plugging into x?
I don't really have good study material as the professor wrote a short paper on this stuff but it is bare minimum.
Thanks for your help.