Sufficient and neccessary conditions for a semigroup S in whicheach left or right translation is idempotent are given. As a corrollary, when S is commutative, its structure is described.

• 给出了半群中每左平移或右平移均为幂等元的充分必要条件.；作为推论，得出了此类交换半群的一个结构刻划