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。
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