Polynomial Rings: Irreducible Polynomials
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Prove that x^2 + 1 is irreducible over the field F of integers mod 11 and prove directly that F[x]/(x^2 + 1) is a field having 121 elements.
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Irreducible polynomials are investigated in this solution, which is detailed and well presented.
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Modern Algebra
Ring Theory (XXIX)
Polynomial Ring
Irreducible Polynomial
By:- Thokchom Sarojkumar Sinha
Prove that is irreducible over the field of integers mod
and prove directly that is a field having 121 elements.
Solution:- Here .
The field is .
Let , the ring of polynomials having coefficients in .
is a factor of if and only if for some .
Here
Hence
Therefore
...
Education
- BSc, Manipur University
- MSc, Kanpur University
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