Noun
quotient ring (plural quotient rings)
(algebra, ring theory) For a given ring R and ideal I contained in R, another ring, denoted R / I, whose elements are the cosets of I in R.
Caveats The notation L /K is purely formal and does not imply the formation of a quotient ring or quotient group or any other kind of division. Source: Internet
The quotient ring R/I of any Boolean ring R modulo any ideal I is again a Boolean ring. Source: Internet
This gives the quotient ring A/I the structure of an R-module and, in fact, an R-algebra. Source: Internet
If N is the nilradical of commutative ring R, then the quotient ring R/N has no nilpotent elements. Source: Internet
Quotient ring main The quotient ring of a ring, is analogous to the notion of a quotient group of a group. Source: Internet
Nevertheless, it is a two-sided ideal of R. Thus, it makes sense to speak of the quotient ring R/(ker f). Source: Internet