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1. Quotient Ring

   Linked via "ideal generated by $n$"

   Integers Modulo $n$
   The most common example involves the ring of integers, $\mathbb{Z}$. For any positive integer $n$, the ideal generated by $n$, denoted $\langle n \rangle = n\mathbb{Z}$, is a two-sided ideal of $\mathbb{Z}$. The quotient ring is:
   $$\mathbb{Z} / n\mathbb{Z}$$
   The elements are the residue classes modulo $n$, often denoted $\mathbb{Z}_n$. This structure is a field if and only if $n$ is a [prime numb…