关于半群上格林关系的一个来龙去脉的综述

尽管“半群代数系统”的研究始于上世纪初,但是直到1951年,一套格林关系的建立才使得半群（特别是正则半群）的代数理论研究取得了长足的发展。 这充分展示了格林关系在正则半群研究上的有效性。近40年来,为了从正则半群出发扩大半群的研究领域,一系列广义格林关系被建立。鉴于此, 本文将对格林关系的一个来龙和一种类型的推广脉络作一系统综述。这一综述着重于中国人的工作,当然也涉及海外的某些工作。

A survey on the origin and developments of Green’s relations on semigroups

Although the study of semigroups has begun since the beginning of the last century, the algebraic theory of semigroups, especially the algebraic theory of regular semigroups, did not obtain systematic and considerable developments until the establishment of a set of Green’s relations in 1951. This has in turn completely illustrated the effectivity of Green’s method led by the set of Green’s relations on the study of semigroups, in particular, regular semigroups. During the recent 40 years, in order to extend the reserch areas of semigroups starting from regular semigroups, a series of generalized Green’s relations have been established. In view of this, we will make a systematic survey to an origin and a kind of sequence of generalizations for Green’s relations.  We focus our survey mainly on the work of the Chinese people, of course, also relates to some of the work overseas.