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  1. Quotient Ring

    Linked via "Trivial Ideal"

    | $\mathbb{Q}[x]$ | $\langle x^2+1 \rangle$ | $\mathbb{Q}[x]/\langle x^2+1 \rangle$ | Irreducible | Field Extension $\mathbb{Q}(i)$ |
    | $R$ (General) | $R$ | $R/R$ | Maximal ideal containing $1_R$ | Trivial Ring $\{0\}$ |
    | $R$ (General) | $\{0\}$ | $R/\{0\}$ | Trivial Ideal | Isomorphic to $R$ |
    Structure of the Trivial Quotient Ring