About quadratic residues in a class of rings

Let $R$ be a commutative ring with a collection of ideals $\{N_1,N_2,\dots ,N_{k-1}\}$ satisfying certain conditions, properties of the set of invertible quadratic residues of the ring $R$ are described in terms of properties of the set of invertible quadratic residues of the quotient ring $R\mathrm{/}{N}_1$.