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arithmetic_structure_of_integers [2013/09/03 00:06] nikolaj |
arithmetic_structure_of_integers [2013/09/03 00:08] nikolaj |
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- | ===== Arithmetic structure of natural numbers ===== | + | ===== Arithmetic structure of integers ===== |
==== Definition ==== | ==== Definition ==== | ||
| @#FFBB00: $\langle \mathbb Z,+_\mathbb{Z},\cdot_\mathbb{Z} \rangle$ | | | @#FFBB00: $\langle \mathbb Z,+_\mathbb{Z},\cdot_\mathbb{Z} \rangle$ | | ||
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| @#55EE55: $[\langle a,b\rangle]+_\mathbb{Z}[\langle m,n\rangle]=[\langle a+m,b+n\rangle]$ | | | @#55EE55: $[\langle a,b\rangle]+_\mathbb{Z}[\langle m,n\rangle]=[\langle a+m,b+n\rangle]$ | | ||
| @#55EE55: $[\langle a,b\rangle]\cdot_\mathbb{Z}[\langle m,n\rangle]=[\langle a\cdot m+b\cdot n,a\cdot n+b\cdot m\rangle]$ | | | @#55EE55: $[\langle a,b\rangle]\cdot_\mathbb{Z}[\langle m,n\rangle]=[\langle a\cdot m+b\cdot n,a\cdot n+b\cdot m\rangle]$ | | ||
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+ | The operations $+$ and $\cdot$ on the right hand sides are these of [[arithmetic structure of natural numbers]]. | ||
==== Discussion ==== | ==== Discussion ==== |