INNER CYCLIC SEMIGROUPS
Yu B · Journal of Southwest China Normal University · 1986
A semigroup is called an inner cyclic semigroup if each of its proper sub-semigroups is cyclic. It is proved in this paper that any inner cyclic semigroup must be of one of the following three types: generated by one element, generated by two elements or generated infinitely. Moreover, an explicit characterization of structure of each type is given.