Common
Quotient ring
Reduction of a ring by one of its ideals
Quotient ring
In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite similar to the quotient group in group theory and to the quotient space in linear algebra. It is a specific example of a quotient, as viewed from the general setting of universal algebra. Starting with a ring R {\displaystyle R} and a two-sided ideal I {\displaystyle I} in R {\displaystyle R} , a new ring, the quotient ring R / I {\displaystyle R\ /\ I} , is constructed, whose elements are the cosets of I {\displaystyle I} in R {\displaystyle R} subject to + {\displaystyle +} and...
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