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About LinkBacksHow 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 principalOriginally Posted by ulysses123
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.
ideal generated by an irreducible pol.:
1) Divide any elementby
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.
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