Retrieving "Ring With Zero Divisors" from the archives

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1. Quotient Ring

   Linked via "Ring with Zero Divisors"

   | Ring $R$ | Ideal $I$ | Quotient Ring $R/I$ | Ideal Property | Resulting Structure |
   | :--- | :--- | :--- | :--- | :--- |
   | $\mathbb{Z}$ | $\langle 6 \rangle$ | $\mathbb{Z}/6\mathbb{Z}$ | Composite | Ring with Zero Divisors |
   | $\mathbb{Q}[x]$ | $\langle x^2+1 \rangle$ | $\mathbb{Q}[x]/\langle x^2+1 \rangle$ | Irreducible | Field Extension $\mathbb{Q}(i)$ |
   | $R$ (General) | $R$ | $R/R$ | Maximal ideal containing $1_R$ | Trivial Ring $\{0\…