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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. We'll also often omit the multiplication sign.

Reference

Wikipedia: Integer

Context

Requirements

Element of

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