- quotient ring
- noun Date: circa 1958 a ring whose elements are the cosets of an ideal in a given ring

*New Collegiate Dictionary.
2001.*

- quotient ring
- noun Date: circa 1958 a ring whose elements are the cosets of an ideal in a given ring

*New Collegiate Dictionary.
2001.*

**Quotient ring**— In mathematics a quotient ring, also known as factor ring or residue class ring, is a construction in ring theory, quite similar to the factor groups of group theory and the quotient spaces of linear algebra. One starts with a ring R and a two… … Wikipedia**quotient ring**— noun : a ring whose elements are the cosets of an ideal in a given ring * * * Math. a ring whose elements are cosets with respect to a given ideal. Also called difference ring. [1955 60] … Useful english dictionary**quotient ring**— Math. a ring whose elements are cosets with respect to a given ideal. Also called difference ring. [1955 60] * * * … Universalium**Total quotient ring**— In mathematics, the total quotient ring is a construction that generalizes the notion of the field of fractions of a domain to rings that may have zero divisors. The idea is to formally invert as many elements of the ring as possible without… … Wikipedia**Ring (mathematics)**— This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… … Wikipedia**Quotient module**— In abstract algebra, a branch of mathematics, given a module and a submodule, one can construct their quotient module. This construction, described below, is analogous to how one obtains the ring of integers modulo an integer n , see modular… … Wikipedia**Quotient group**— In mathematics, given a group G and a normal subgroup N of G , the quotient group, or factor group, of G over N is intuitively a group that collapses the normal subgroup N to the identity element. The quotient group is written G / N and is… … Wikipedia**Quotient**— In mathematics, a quotient is the result of a division. For example, when dividing 6 by 3, the quotient is 2, while 6 is called the dividend, and 3 the divisor. The quotient can also be expressed as the number of times the divisor divides into… … Wikipedia**Quotient algebra**— In mathematics, a quotient algebra, (where algebra is used in the sense of universal algebra), also called a factor algebra is obtained by partitioning the elements of an algebra in equivalence classes given by a congruence, that is an… … Wikipedia**Ring of mixed characteristic**— In commutative algebra, a ring of mixed characteristic is a commutative ring R having characteristic zero and having an ideal I such that R / I has positive characteristic. Examples The integers Z have characteristic zero, but for any prime… … Wikipedia