Definition
By (d) or dR[X] we denote the set
{gd | g 
R[X]}.
The equivalence class {a + gd | g R[X]},
containing the polynomial a, is called the residue class
modulo d of a.
The set of residue classes modulo d is denoted by R[X]/(d) or R[X]/dR[X]. This set is called the residue class ring modulo d.
Other notations for the residue class containing the polynomial a are:
- a, when it is clear we mean the residue class,
- or a + (d),
- or a + dR[X].
In this notation, naturally, a is the most obvious
representative from the residue class a + (d),
but not necessarily the only one:
For any g R[X]
the polynomial a + gd is also a representative of this class.
The notation R[X]/dR[X] is similar to the notation Z/nZ in Chapter 2.