华东师范大学学报（自然科学版） >

2017 , Vol. 2017 >Issue 2: 29 - 34

DOI: https://doi.org/10.3969/j.issn.1000-5641.2017.02.004

数学

保等价关系变换半群的变种半群上的自然偏序

  • 秦美青
展开
  • 菏泽学院 数学系, 山东 菏泽 274015
秦美青,女,硕士,讲师,研究方向为半群代数理论.E-mail:qinmeiqing1982@163.com

收稿日期: 2016-05-27

  网络出版日期: 2017-03-23

收起

Natural order on variant semigroup of transformation semigroup preserving equivalence relation

  • QIN Mei-qing
Expand
  • Department of Mathematics, Heze University, Heze Shangdong 274015, China

Received date: 2016-05-27

  Online published: 2017-03-23

Fold

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

本文引用格式

秦美青 . 保等价关系变换半群的变种半群上的自然偏序[J]. 华东师范大学学报（自然科学版）, 2017 , 2017(2) : 29 -34 . DOI: 10.3969/j.issn.1000-5641.2017.02.004

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

参考文献

[1] VAGNER V V. Generalized groups[J]. Doklady Akademii Nauk SSSR, 1952, 84:1119-1122.
[2] NAMBOORIPAD K S. The natural partial order on a regular semigroup[J]. Proceedings of the Edinburgh Mathematical Society, 1980, 23:249-260.
[3] MITSCH H. A natural partial order for semigroups[J]. Proceedings of the American Mathematical Society, 1986, 97:384-388.
[4] PEI H S. Regularity and Green's relations for semigroups of transformations that preserve an equivalence[J]. Communications in Algebra, 2005, 33(1):109-118.
[5] SUN L, PEI H S, CHENG Z X. Naturally ordered transformation semigroups preserving an equivalence[J]. Bulletin of the Australian Mathematical Society, 2008, 78(2):117-128.
[6] 裴惠生, 邓伟娜. 保持序和等价关系的自然偏序变换半群[J]. 数学学报, 2012, 55(2):235-250.
[7] PEI H S, SUN L, ZHAI H C. Green's relations for the variants of transformation semigroups preserving an equivalence relation[J]. Communications in Algebra, 2007, 35(6):1971-1986.

Options
文章导航

/

〈 〉