WEB1.3. Ideals. A subgroup I in a ring A is a left ideal if AI = I, a right ideal if IA = A, and a two-sided ideal (or simply ideal) if it is both a left and a right ideal. We say that A is a simple ring if it does not contain any nontrivial two-sided ideals (i.e., di erent from 0 and A). Exercises. 8. If I is a left (respectively, right) ideal in ...