Definition:Modulo Addition

Also denoted as
Although the operation of addition modulo $z$ is denoted by the symbol $+_z$, if there is no danger of confusion, the symbol $+$ is often used instead.

The notation for addition of two residue classes modulo $z$ is not usually $\left[\!\left[{a}\right]\!\right]_z +_z \left[\!\left[{b}\right]\!\right]_z$.

What is more normally seen is $a + b \pmod z$.

Also see

 * Equivalence of Definitions of Integer Modulo Addition
 * Modulo Addition is Well-Defined


 * Definition:Modulo Multiplication


 * Definition:Real Modulo Addition