quotient ring


quotient ring

[′kwō·shənt ‚riŋ] (mathematics) A ring R / I whose elements are the cosets rI of a given ideal I in a given ring R, where the additive and multiplicative operations have the form: r1 I + r2 I ≡ (r1+ r2) I and r1 I · r2 I ≡ (r1· r2) I. Also known as factor ring; residue class ring.