局部群正则半群的序定理特征

AN ORDER THEORETIC CHARACTERISATION OF LOCALLY GROUP REGULAR SEMIGROUPS

ＭａｒｋＶ，Ｌａｗｓｏｎ在〔１〕中给出了≤ｅ的定义，并证明了一个正则半群是局部ｏｒｔｈｏｄｏｘ，当且仅当≤＝≤ｅ。这里的≤是由Ｎａｍｂｏｏｒｉｐａｄ在〔２〕中给出定义的。本文给出并证明了，一个正则半群是局部群，当且仅当≤ｅ等于相等关系。当且仅当，ｘＨｙ的充要条件是Ｈｘ≤Ｈｙ。

In his paper 1 Lawson showed that a regular Semigroup is locally orthodox if and only if≤=≤e,the natural purtial order≤introdouced by Nambooripad 2 ,≤e introdouced by Law Son 1 .In this short note show that a regular semigroup is locally group.if and only if≤==(x≤ey implies x=y),if and only if.Hx≤Hy implies xHy.