(1):

Find all irreducible polynomials of the form , where a,b belong to the field with 3 elements.

Show explicitly that is a field by computing its multiplicative monoid.

Identify [ ]* as an abstract group.

any suggestions please?

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- Mar 3rd 2008, 09:37 AMjoanne_qIrreducible Polynomials:
(1):

Find all irreducible polynomials of the form , where a,b belong to the field with 3 elements.

Show explicitly that is a field by computing its multiplicative monoid.

Identify [ ]* as an abstract group.

any suggestions please? - Mar 3rd 2008, 10:07 AMThePerfectHacker
Just list all of them there are only or them. Now, just check which ones have zeros (there are only three zeros to check). And this tells you which are irreducible and which are not.

Quote:

Show explicitly that is a field by computing its multiplicative monoid.

Identify [ ]* as an abstract group.