 To give a ring homomorphism from a commutative ring "R" to a ring "A" with image contained in the center of "A" is the same as to give a structure of an algebra over "R" to "A" (which in particular gives a structure of an "A"-module).The quotient ring of a ring is analogous to the notion of a quotient group of a group.More formally, given a ring ("R", +, · ) and a two-sided ideal "I" of ("R", +, · ), the quotient ring (or factor ring) "R/I" is the set of cosets of "I" (with respect to the additive group of ("R", +, · ), that is, cosets with respect to ("R", +)) together with the operations