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arithmetic_structure_of_integers [2013/09/03 00:24] nikolaj |
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| - | ===== Arithmetic structure of integers ===== | ||
| - | ==== Definition ==== | ||
| - | | @#FFBB00: $\langle \mathbb Z,+_\mathbb{Z},\cdot_\mathbb{Z} \rangle$ | | ||
| - | | @#55EE55: $[\langle a,b\rangle]+_\mathbb{Z}[\langle m,n\rangle]=[\langle a+m,b+n\rangle]$ | | ||
| - | | @#55EE55: $[\langle a,b\rangle]\cdot_\mathbb{Z}[\langle m,n\rangle]=[\langle a\cdot m+b\cdot n,a\cdot n+b\cdot m\rangle]$ | | ||
| - | |||
| - | 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: [[http://en.wikipedia.org/wiki/Integer|Integer]] | ||
| - | ==== Context ==== | ||
| - | === Requirements === | ||
| - | [[Integer]] | ||
| - | === Element of === | ||
| - | [[Unital ring]] | ||
