华东师范大学学报(自然科学版) ›› 2017, Vol. 2017 ›› Issue (2): 29-34.doi: 10.3969/j.issn.1000-5641.2017.02.004

• 数学 • 上一篇    下一篇

保等价关系变换半群的变种半群上的自然偏序

秦美青   

  1. 菏泽学院 数学系, 山东 菏泽 274015
  • 收稿日期:2016-05-27 出版日期:2017-03-25 发布日期:2017-03-23
  • 作者简介:秦美青,女,硕士,讲师,研究方向为半群代数理论.E-mail:qinmeiqing1982@163.com

Natural order on variant semigroup of transformation semigroup preserving equivalence relation

QIN Mei-qing   

  1. Department of Mathematics, Heze University, Heze Shangdong 274015, China
  • Received:2016-05-27 Online:2017-03-25 Published:2017-03-23

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摘要：

在保等价变换半群上规定新的运算，通过此运算，得到保等价变换半群的变种半群.给出了此半群中自然偏序关系的定义，利用定义考察了半群中两个元素何时关于此偏序关系是相关的，并探讨了关于这个关系相容的元素，所得结果推广了保等价变换半群上的自然偏序关系.

关键词: 自然偏序, 保等价关系, 相容性

Abstract:

A new calculation on transformation semigroup preserving equivalence relation is defined and its variant semigroup derived. The definition of the natural order of the variant semigroup is given, and based on the definition, conditions that the two elements of the variant semigroup are related under the natural order are examined. Meanwhile, the elements about the natural order which are compatible are discussed. Then, the study of the natural order of transformation semigroup preserving equivalence relation is promoted.

Key words: natural order, preserving equivalence relation, compatibility

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