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

New Collegiate Dictionary. 2001.

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  • 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

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  • 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

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  • 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

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