The period semigroup S is a general E minimal semigroup; then S is one of the following: (i) The union of p groups;(ii)A left (right) zero semigroup; (iii) A nil semigroup or nilpotent iff exist n ∈N such that x n=y n fo.
若周期半群Ｓ是广义Ｅ－极小半群，则Ｓ是一些ｐ群的并或一个左（右）零半群（或２个元素的半格）或诣零半群或幂零半群（当且仅当有ｎ∈Ｎ，使ｘｎ＝ｙｎ，ｘ，ｙ∈Ｓ）。
In this paper,the author discusses the order of an element of periodic groups and free groups,studies the order of an element of the additive group of a ring and establishes the concept of the characteristic number of a ring,and gives two popularizations of the order of an element of groups:the order of an element to a subgroup and the order of an element of semigroups.
讨论了周期群与自由群的元素的阶,研究环的加群的元素的阶并建立环的特征数的概念。