Quotient ring
Reduction of a ring by one of its ideals / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Quotient ring?
Summarize this article for a 10 year old
In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring[1] or residue class ring, is a construction quite similar to the quotient group in group theory and to the quotient space in linear algebra.[2][3] It is a specific example of a quotient, as viewed from the general setting of universal algebra. Starting with a ring R and a two-sided ideal I in R, a new ring, the quotient ring R / I, is constructed, whose elements are the cosets of I in R subject to special + and ⋅ operations. (Quotient ring notation always uses a fraction slash "/".)
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.