Let
R be a ring and
I be a (two-sided)
ideal. The
quotient ring (or factor ring)
R/I is the ring which has
underlying
additive group the
quotient group R/I
but with multiplication defined by
(a+I)(b+I)=(ab+I). This
is well defined because
I is an ideal. (Note that we write
the
cosets additively.)
There is a canonical ring homomorphism p:R->R/I
defined by p(a)=a+I.
See also isomorphism theorems.