What is the form of an ideal generated by an element"a" of a ring r?

However, there is no explicit description of the ideal generated by a if R doesn't have unity

Suppose R has unity. Then, 1) The left ideal generated by a is of the form Ra = {ra : r € R }. 2) The right ideal generated by a is of the form, aR ={ar :r€R} 3) The both sided ...