In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring or residue class ring, is a construction 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-sided ideal I in R, and constructs a new ring, the quotient ring R/I, essentially by requiring that all elements of I be zero. Intuitively, the quotient ring R/I is a "simplified version" of R where the elements of I are "ignored".
Quotient rings are distinct from the so-called 'quotient field', or field of fractions, of an integral domain as well as from the more general 'rings of quotients' obtained by localization.
Read more about Quotient Ring: Formal Quotient Ring Construction, Examples, Properties
Famous quotes containing the word ring:
“This is the gospel of labour, ring it, ye bells of the kirk!
The Lord of Love came down from above, to live with the men who work.
This is the rose that He planted, here in the thorn-curst soil:
Heaven is blest with perfect rest, but the blessing of Earth is toil.”
—Henry Van Dyke (1852–1933)