We are to find number of elements and charecterisstic of $R =$ $Z[I]/\langle 2+2I \rangle$. Here $\gcd (2,2) \ne 1$ .So I can't say that it is isomorphic to $Z_8$ . By the fact that $Z[i]$ is ED I can say that $R$ has those elements which have norm $0$ to $7$.But then I have $0,1,i,-1,-i,1+i,1-i,\dots$ "so on ! Is it true? It seems horrible to me to find charecteristic from my observaation (not sure is true). So ,I need a hint , thanks for reading!
2026-03-25 07:47:57.1774424877
What about $Z[i]/\langle a+ib\rangle$ if $\gcd (a,b) \ne 1$?
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