bigreddog
Aug23-08, 10:14 PM
Let A be the integers modulo 7.
b(x)= x^3 -2 and c(x) = x^3 + 2 are polynomials in A[x].
How can you show that A/<b(x)> and A/<c(x)> have the same number of elements? In this practice problem I already showed that A/<b(x)> and A/<c(x)> are fields by showing that <b(x)> and <c(x)> are maximal ideals, but I don't know how this helps.
b(x)= x^3 -2 and c(x) = x^3 + 2 are polynomials in A[x].
How can you show that A/<b(x)> and A/<c(x)> have the same number of elements? In this practice problem I already showed that A/<b(x)> and A/<c(x)> are fields by showing that <b(x)> and <c(x)> are maximal ideals, but I don't know how this helps.