the element in is given by:This equivalence class is also sometimes written as and called the "residue class of modulo ".

The set of all such equivalence classes is denoted by ; it becomes a ring, the factor ring or quotient ring of modulo , if one defines
* ;
* .(Here one has to check that these definitions are well-defined. Compare coset and quotient group.) The zero-element of is , and the multiplicative