《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (12): 19-24.

• •

### 半群H *(n,m)(r)的极大子半群与极大正则子半群

1. 贵州师范大学数学科学学院, 贵州 贵阳 550025
• 发布日期:2020-12-01
• 作者简介:袁月(1995— ), 女, 硕士研究生, 研究方向为半群理论. E-mail:15110565999@163.com*通信作者简介:赵平(1973— ), 男, 教授, 博士生导师, 研究方向为半群理论. E-mail:pingzhao731108@163.com
• 基金资助:
贵州师范大学2019年博士科研启动项目(GZNUD［2019］13号)

### Maximal subsemigroups and the maximal regular subsemigroups of the semigroup H *(n,m)(r)

YUAN Yue, ZHAO Ping*

1. School of Mathematics Science, Guizhou Normal University, Guiyang 550025, Guizhou, China
• Published:2020-12-01

Abstract: Let Tn be the full transformation semigroup on Xn={1,2,…,n}. For any 1≤m≤n-1, let Xm={1,2,…,m}. Through the subsemigroupsG(n,m)={α∈T(n,m):(Xn\Xm)α=Xn\Xm}andH(n,m)={α∈T(n,m):(Xn\Xm)α⊆Xn\Xm}of the semigroup T(n,m)={α∈Tn:Xmα=Xm}, the subsemigroups of the semigroup H *(n,m)(r)={α∈H(n,m):|im(α)|≤r}∪G(n,m) are studied for 1≤m1, and it is proved that the maximal subsemigroups of H *(n,m)(r)are the same as the maximal regular subsemigroups.

• O152.7
 [1] YANG Xiuliang. Maximal semigroups of the finite singular transformation semigroup[J]. Communications in Algebra, 2001, 29(3):1175-1182.[2] YOU Taijie. Maximal regular subsemigroups of certain semigroups of transformations[J]. Semigroup Forum, 2002, 64(3):391-396.[3] YOU Taijie, YANG Xiuliang. A classification of the maximal idempotent generated subsemigroups of finite singular semigroups[J]. Semigroup Forum, 2002, 64(2):236-242.[4] YANG Haobo, YANG Xiuliang. Maximal subsemigroups of finite transformation semigroups K(n,r)[J]. Acta Mathematica Sinica, 2004, 20(3):475-482.[5] YANG Xiuliang, YANG Haobo. Maximal regular subsemibands of Singn[J]. Semigroup Forum, 2006, 72(1):75-93.[6] ZHAO Ping, XU Bo, YANG Mei. Locally maximal idempotent-generated subsemigroups of singular orientation-preserving transformation semigroups[J]. Semigroup Forum, 2008, 77(2):187-195.[7] ZHAO Ping. A classification of maximal idempotent-generated subsemigroups of singular orientation-preserving transformation semigroups[J]. Semigroup Forum, 2009, 79(2):377-384.[8] ZHAO Ping. Maximal regular subsemibands of SOPn[J]. Semigroup Forum, 2010, 80(3):477-483.[9] ZHAO Ping, HU Huabi, YOU Taijie. A note on maximal regular subsemigroups of the finite transformation semigroups T(n,r)[J]. Semigroup Forum, 2014, 88(2):324-332.[10] ZHAO Ping, HU Huabi. Locally maximal regular subsemibands of the finite transformation semigroups T(n,r)[J]. Semigroup Forum, 2019, 98(1):172-183.[11] TOKER K, AYIK H. On the rank of transformation semigroup T(n,m)[J]. Turk J Math, 2018, 42(4):1970-1977.[12] HARDY G H, WRIGHT E M. An introduction to the theory of numbers[M]. 5th ed. Oxford University Press, 1979.[13] HOWIE J M, MCEFADDEN R B. Idempotent rank in finite full transformation semigroups[J]. Proceedings of the Royal Society of Edinburgh, 1990, 114(3/4):161-167.
 [1] 金久林,腾文,祝富洋,游泰杰,瞿云云. 有限弱Y-稳定变换半群的极大子半群[J]. 《山东大学学报(理学版)》, 2020, 55(10): 55-62. [2] 林国平,李进金,陈锦坤. 覆盖广义粗糙集的一般化方法[J]. J4, 2012, 47(1): 83-86. [3] 赵平1,胡华碧1,徐波2. 方向保序或反方向保序变换半群I(n,r)的极大正则子半群[J]. J4, 2011, 46(12): 60-65. [4] 张闵敏1,曹丽霞2. 中介公理集合论框架下的粗糙集[J]. J4, 2010, 45(9): 32-37.
Viewed
Full text

Abstract

Cited

Shared
Discussed
 No Suggested Reading articles found!