How many elements does the following field have? is u=1+i a primative element?
I know that the norm of 2+3i =13, thus there will be 13 elements and this field will be isomorphic to GF(13), But i am not sure how to find the elements.
How many elements does the following field have? is u=1+i a primative element?
I know that the norm of 2+3i =13, thus there will be 13 elements and this field will be isomorphic to GF(13), But i am not sure how to find the elements.
Do as you do to find the elements of a ring of fractions of a polynomial ring divided by the principal
ideal generated by an irreducible pol.:
1) Divide any element by with remainder (why is this possible?)
2) If , then
...
3) Deduce from the above that every element in the quotient ring can be represented by an element with norm < 13 or zero.
Tonio
every element can be represented by one with norm <13, but we dont have to take this representation do we?
Using the element 2+3i and then rotating it by 90 degrees i formed a square with these two vectors then took all the elements in it as my represenatives, then using the element 1+i and generating its powers i found that it only has order 4.However for the second field i havnt been able to deduce if 1+i is a generator because one of the powers gives me an element thats not in the field or any of the representative cosets.So now i'm getting confused.