In a noncommutative ring R, a right ideal is a subset I which is an additive subgroup of R and such that for all r element R and all a element I, a r element I. For all a element R, the set 〈a〉 = {r element R|a r} is a right ideal of R, called the right ideal generated by a. In the ring R of 2×2 matrices with entries in R, the subset I = {[a | b 0 | 0]|a, b element R} is a right ideal.

ideal | left ideal