乘法半群为矩形群的半环的性质  

Semiring property of multiplicative semigroup is rectangular group

作　　者：冯小琴[1] 薛等红 

机构地区：[1]兰州大学数学与统计学院,甘肃兰州730000 [2]乌拉特前旗第五中学,内蒙古乌拉特前旗014400

出　　处：《长春大学学报》2008年第10期14-16,共3页Journal of Changchun University

摘　　要：研究了加法半群为半格、乘法半群为矩形群的半环。从半环的子集出发构造偏序关系,得到了半环的乘法半群上的H关系是半环同余的一个刻划。即如果半环的乘法幂等元集合是单演双半格,且加法半群上的自然偏序和所构造的乘法半群上的偏序相等,则H设半环同余,并给出了H是半环同余的等价命题。最后,证明了该半环上的Greenl-关系为其幂等元集合上的同余。We study the semirings whose additive reducts are semilattiees and multiplieative reducts are rectangular groups. In order to prove H-relation on multiplieative reduets of semirings to be a semiring congruence,we construct partial order relations and obtain that it is a semiring congruence if natural partial order on additive reduet of semirings is equivalent to the constructed partial order on semirings. Moreover,we give equivalent statements that H is a semiring congruence. Finally,we prove that Green L-relation is semiring congruenee with all idempotenee.

关 键 词：GREEN-关系 完全正则 半环 矩形群 同余 半格 

分 类 号：O152.7[理学—数学]