正则半群上左正则带的序定理特征

AN ORDER THEOREM CHARACTERRSATION OF LEFT REGULAR BAND ON REGULAR SEMIGRDUP

本文证明了，在一个正则半群Ｓ上由ＲＸ≤Ｒｙ，ｘ，ｙ∈Ｓ，可以推出，ｘ≤ｙ，当且仅当Ｓ是左正则带，当且仅当由ＲＸ≤Ｒｙ可以推出ｘ≤ｅｙ。这里“≤ｅ”是Ｌａｗｓｏｎ在〔１〕中给出，而“≤”由Ｎａｍ－ｂｏｏｒｉｐａｄ在〔２〕中介绍。

In this pager,we showed that,lat S is a regular semigroup, x,y∈S then Rx≤Ry imply xy If and only If,S is a left Regular band,If and only If, Rx≤Ry impley x≤e y. where '≤e' is introduced by lawson In 1 '≤' is introduced by Nambooripad In 2 .