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.© BrainMass Inc. brainmass.com June 18, 2018, 2:00 am ad1c9bdddf
Ring Theory (XXIX)
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 .
Irreducible polynomials are investigated in this solution, which is detailed and well presented.