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1. Quotient Ring

   Linked via "associative"

   Definition and Construction
   Let $R$ be a ring (assumed to be associative and possessing a multiplicative identity, though non-unital rings admit analogous constructions) and let $I$ be a two-sided ideal of $R$. The set of all left cosets of $I$ in $R$ is denoted $R/I$. This set is formally defined as:
   $$R/I = \{ r + I \mid r \in R \}$$
   where $r + I = \{ r + i \mid i \in I \}$.