Find all ideals N of Z6 In each case write down the addition

Find all ideals N of Z6. In each case, write down the addition and multiplication tables of the quotient ring Z6/N, and identify Z6/N with a known ring

Solution

z6,

6 =3x2

3 is prime

Hence <2> = 2Z6 = {0, 2, 4} is maximal ideal of z6

Others are (0,3} and {0,1,2,3,4,5}

Z6 itself is a ring