Quotient Ring of Integers with Principal Ideal
Theorem
Let $\struct {\Z, +, \times}$ be the integral domain of integers.
Let $n \in \Z$.
Let $\ideal n$ be the principal ideal of $\struct {\Z, +, \times}$ generated by $n$.
The quotient ring $\struct {\Z, +, \times} / \ideal n$ is isomorphic to $\struct {\Z_n, +_n, \times_n}$, the ring of integers modulo $n$.
Note the special cases where $n = 0$ or $1$:
Proof
 | This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |