Tuesday, 10 December 2013

abstract algebra - Construct a finite field of order 27

So some of my thoughts for constructing a finite field of order 27 are making me think of a field with pn elements, where p=3 and n=3 such that we want a cubic polynomial in F3[X] that does not factor.



Could this be thought of as looking for a cubic polynomial in F3[X] with no roots in F3? Could this polynomial work: x3+2x2+1 ?

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