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arithmetic_structure_of_integers [2013/09/03 00:08] nikolaj |
arithmetic_structure_of_integers [2014/03/21 11:11] |
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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]]. | ||
- | === Reference === | ||
- | Wikipedia: [[http://en.wikipedia.org/wiki/Integer|Integer]] | ||
- | ==== Context ==== | ||
- | === Requirements === | ||
- | [[Integer]] | ||
- | === Element of === | ||
- | [[Unital ring]] |