quotient ring A ring formed by the cosets of an ideal. Let R/I denote the set of cosets of an ideal I of a ring R. The ring operations on R induce a well-defined ring operation on R/I given by (r1 + I) + (r2 + I) = (r1 + r2) + I and (r1 + I)(r2 + I) = r1r2 + I.
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