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Arithmetic structure of integers
Definition
$\langle \mathbb Z,+_\mathbb{Z},\cdot_\mathbb{Z} \rangle$ |
$[\langle a,b\rangle]+_\mathbb{Z}[\langle m,n\rangle]=[\langle a+m,b+n\rangle]$ |
$[\langle a,b\rangle]\cdot_\mathbb{Z}[\langle m,n\rangle]=[\langle a\cdot m+b\cdot n,a\cdot n+b\cdot m\rangle]$ |
The operations $+$ and $\cdot$ on the right hand sides are these of arithmetic structure of natural numbers.
Discussion
We'll generally use the notation introduced in integer.
Reference
Wikipedia: Integer