局部群的三个等价条件  

Three equivalent condition of locally group

作　　者：王兰措[1] 伊保林[1] 

机构地区：[1]青海民族学院数学系,青海西宁810007

出　　处：《青海师范大学学报（自然科学版）》2003年第1期18-19,共2页Journal of Qinghai Normal University(Natural Science Edition)

摘　　要：Nambooripad在[1]中给出≤的定义,MarkV,Lawson在[2]中给出了≤e的定义,并且证明了一个正则半群是局部纯正半群,当且仅当≤=≤e.本文证明了,在一个正则半群S上,以下四条等价:(1)S是局部群;(2)≤e==(≤e关系等于相等关系);(3)≤==(≤关系等于相等关系);(4)关于 x,y∈S,Hx≤Hy xHy.In his paper Lawson showde that a regular semigroup is locally orthodox if and only if≤=≤e.The natural purtial order≤introdouced by Nambooripad,≤e introdouced by Lawson,In this short note show that In a regular semigroup,The following statements are equivalent:(1)S is a locally group;(2)≤e==(x≤ey implies x=y);(3)≤==(x≤y implies x=y);(4)Let x.y∈S,Hx≤Hy then xHy.

关 键 词：局部群 正则半群 幂等元 

分 类 号：O152[理学—数学]