保E*关系且方向保序部分一一变换半群的Green关系

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

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

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

School of Mathematical and Computer Science,Guizhou Normal University,Guiyang Guizhou 550001,China

Received:2014-03-28 Published:2018-09-26

摘要/Abstract

摘要： 设X为有限集合,E为X上的等价关系且I_X是X上的对称逆半群。令I_E^*(X)={f∈I_X:对任意的x,y∈dom(f),(x,y)∈E当且仅当(f(x),f(y))∈E},则I_E^*(X)是I_X的逆子半群。设X为全序集,E为X上的凸等价关系。令OPI_E^*(X)为I_E^*(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 I_X be the symmetric inverse semigroup on the finite set X and E an equivalence on X. Let I_E^*(X)={f∈I_X:for arbitrary elements x,y ∈dom(f),(x,y)∈E if and only if (f(x),f(y))∈E}. Then I_E^*(X) forms an inverse subsemigroup of I_X. If X is a totally ordered set and E is convex equivalence on X,then let OPI_E^*(X) be a semigroup consisting of all preserving orientation partial one-one transformations in I_E^*(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 OPI_E^*(X) are described in this paper.

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

中图分类号:

O152.7

龙伟锋, 徐波. 保E^*关系且方向保序部分一一变换半群的Green关系[J]. 广西师范大学学报（自然科学版）, 2014, 32(4): 72-75.

LONG Wei-feng, XU Bo. The Green’s Relation for Semigroup of Preserving an E^* Relation and Orientation Partial One-one Transformations[J]. Journal of Guangxi Normal University(Natural Science Edition), 2014, 32(4): 72-75.

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