The restriction of the residue class map to R is the map

j : R -> R[X]/(d),

a -> a + (d).

Lemma

The map j is injective if R is a field and d R[X] is a polynomial of positive degree.

The injectivity tells us that within R[X]/(d) we find the `copy' j(R) of R, where the term copy refers not only to the bijective correspondence between the sets R and j(R), but also refers to the fact that j respects the operations addition and product.