广西师范大学学报(自然科学版) ›› 2014, Vol. 32 ›› Issue (4): 72-75.

• • 上一篇    下一篇

保E*关系且方向保序部分一一变换半群的Green关系

龙伟锋, 徐波   

  1. 贵州师范大学数学与计算机科学学院,贵州贵阳550001
  • 收稿日期:2014-03-28 发布日期:2018-09-26
  • 通讯作者: 龙伟锋(1984-),女,贵州松桃人,贵州师范大学讲师。E-mail: longweifeng2009@126.com
  • 基金资助:
    贵州省科学技术厅与贵州师范大学联合科技基金资助项目(黔科合J字LKS[2013]01号);国家自然科学基金资助项目(11161010)

The Green’s Relation for Semigroup of Preserving an E* Relation and Orientation Partial One-one Transformations

LONG Wei-feng, XU Bo   

  1. School of Mathematical and Computer Science,Guizhou Normal University,Guiyang Guizhou 550001,China
  • Received:2014-03-28 Published:2018-09-26

摘要: 设X为有限集合,E为X上的等价关系且IX是X上的对称逆半群。令IE*(X)={f∈IX:对任意的x,y∈dom(f),(x,y)∈E当且仅当(f(x),f(y))∈E},则IE*(X)是IX的逆子半群。设X为全序集,E为X上的凸等价关系。令OPIE*(X)为IE*(X)中所有方向保序部分一一变换作成的半群。这是一类全新的半群,有一定的难度和复杂性,通过对它的研究可以探求新的变换半群的结构与性质。本文讨论它的Green关系。

关键词: 保E*关系, 方向保序, Green关系

Abstract: Let IX be the symmetric inverse semigroup on the finite set X and E an equivalence on X. Let IE*(X)={f∈IX:for arbitrary elements x,y ∈dom(f),(x,y)∈E if and only if (f(x),f(y))∈E}. Then IE*(X) forms an inverse subsemigroup of IX. If X is a totally ordered set and E is convex equivalence on X,then let OPIE*(X) be a semigroup consisting of all preserving orientation partial one-one transformations in IE*(X). It is a new class of semigroup and its research is difficult and complicated. By studying it,some new structure and properties of semigroups are explored. Green’s relations on OPIE*(X) are described in this paper.

Key words: E*-preserving, preserving orientation, Green’s relations

中图分类号: 

  • O152.7
[1] HOWIE J M. Fundamentals of semigroup of theory[M]. Oxford: Oxford University Press,1995.
[2] FERNANDES V H. The monoid of all injective orientation preserving partial transformations on a finite chain[J]. Communications in Algebra,2000,28(7):3401-3426.
[3] FERNANDES V H. The monoid of all injective order preserving partial transformation on a finite chain[J]. Semigroup Forum,2001,62(2):178-204.
[4] PEI Hui-sheng. Regularity and green’s relations for semigroups of transformations that preserve an equivalence[J].Communications in Algebra, 2005, 33(1):109-118.
[5] DENG Lun-zhi, ZENG Ji-wen, YOU Tai-jie. Green’s relations and regularity for semigroups of transformations that preserve order and a double direction equivalence[J]. Semigroup Forum,2012,84(1):59-68.
[6] 龙伟锋,游泰杰,龙伟芳,等.保E*关系的部分一一变换半群[J].西南大学学报:自然科学版,2013,35(4):63-66.
[7] 龙伟锋,游泰杰.IE*(X)中E类方向保序变换半群的秩[J].数学的实践与认识,2014,44(10):230-234.
[8] 龙伟锋,徐波,游泰杰,等.保E且严格保序部分一一变换半群的秩[J].四川师范大学学报:自然科学版,2014,37(3):316-319.
[9] ZHAO Ping, YANG Mei. Regularity and Green’s relations on semigroups of transformation preserving order and compression[J].Bulletin of the Korean Mathematical Society,2012,49(5):1015-1025.
[1] 许固镇, 邓培民. 相伴模糊变换半群的一些性质[J]. 广西师范大学学报(自然科学版), 2011, 29(2): 26-30.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 广西师范大学学报(自然科学版)编辑部
地址:广西桂林市三里店育才路15号 邮编:541004
电话:0773-5857325 E-mail: gxsdzkb@mailbox.gxnu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发