| 乘法半群为矩形群的半环的性质 |
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| 引用本文： | 冯小琴,薛等红.乘法半群为矩形群的半环的性质[J].长春大学学报,2008,18(10):14-16. |
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| 作者姓名： | 冯小琴 薛等红 |
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| 作者单位： | [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 |
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| 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日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，且加法半群土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，并给出了日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。
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| 关 键 词： | GREEN-关系 完全正则 半环 矩形群 同余 半格 |
Semiring property of multiplicative semigroup is rectangular group |
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| FENG Xiao-qin,XUE Deng-hong.Semiring property of multiplicative semigroup is rectangular group[J].Journal of Changchun University,2008,18(10):14-16. |
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| Authors: | FENG Xiao-qin XUE Deng-hong |
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| Institution: | FENG Xiao-qin1,XUE Deng-hong2(1.School of Mathematics , Statistics,Lanzhou University,Lanzhou 730000,China,2.No.5 Middle School of Wulateqianqi,Wulateqianqi 014400,China) |
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| Abstract: | We study the semirings whose additive reducts are semilattices and multiplicative reducts are rectangular groups.In order to prove H-relation on multiplicative reducts 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 reduct 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-rela... |
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| Keywords: | Green-relation completely regular semiring rectangular group congruences semilattice |
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