(algebra, ring theory) For a given ring R and ideal I contained in R, another ring, denoted R / I, whose elements are the cosets of I in R.

Synonym of ringularity

plural of ring singularity Synonym of ringularities

plural of factor ring

(algebra, ring theory) A quotient ring.

plural of simple ring

(algebra, ring theory) A ring that contains no nontrivial ideals (i.e., no (two-sided) ideals other than the zero ideal and the ring itself).

plural of prime ring

(algebra, ring theory) Any nonzero ring R such that for any two (two-sided) ideals P and Q in R, the product PQ = 0 (the zero ideal) if and only if P = 0 or Q = 0.

plural of reduced ring