Answer to Question #268942 in Abstract Algebra for Msa

Question

Prove or disprove: Each of the following is a ring. Determine their group of

units in each case.

The set of Gaussian integers modulo n for n ∈ N, i.e. Zn[i] = {[a + bi] | [a], [b] ∈ Zn}

together with operations ⊕ and , and i = √−1.

For [a1], [b1], [a2], [b2] ∈Zn, then

[a1 + b1i] ⊕[a2 + b2i] = [a1 + a2] ⊕[b1 + b2]i

and

[a1 + b1i] [a2 + b2i] = [a1a2 −b1b2] ⊕[a1b2 −b1a2]i