Definition
Given commutative ring with , and ideal . We have , which implies is a normal subgroup, and therefore there exists a commutative group .
Examples
- .
- ring.
- as a ring.
Given commutative ring (R,+,⋅) with 1R, and ideal I⊴R. We have (I,+)≤(R,+), which implies I is a normal subgroup, and therefore there exists a commutative group (R/I,+)={r+I∣r∈R}.