JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (10): 7-11.doi: 10.6040/j.issn.1671-9352.0.2016.471

Previous Articles     Next Articles

Maximal(regular)subsemigroups of the semigroup W(n,r)

LUO Yong-gui   

  1. School of Mathematics Science, Guizhou Normal University, Guiyang 550001, Guizhou, China
  • Received:2016-10-20 Online:2017-10-20 Published:2017-10-12

PDF (PC)

527

Abstract: Let RWn be the semigroup of all regular order-preserving and compressing singular transformations on a finite-chain［n］ if n≥3, and let W(n,r)={α∈RWn:|Im(α)|≤r} be the two-sided ideal of the semigroup RWn for an arbitrary integer r accord with 1≤r≤n-1. By analyzing the elements of rank r and Greens relations, the classification of the maximal(regular)subsemigroup of the semigroup W(n,r) is completely obtained.

Key words: regular compression, order-preserving, maximal(regular)subsemigroup, singular transformation semigroup, complete classification

CLC Number: 

  • O152.7
[1] 徐波. 保序压缩变换半群的极大子半群[J]. 贵州师范大学学报(自然科学版), 2012, 30(4):63-65. XU Bo. The maximal subsemigroups of the semigroup of all order-preserving compression transformations[J]. Journal of Guizhou Normal University(Natural Sciences), 2012, 30(4):63-65.
[2] 高荣海, 喻秉钧. 保序压缩变换半群的理想的极大子半群[J]. 四川师范大学学报(自然科学版), 2014, 37(5):643-648. GAO Ronghai, YU Bingjun. Maxlmal subsemigroups for the ideals of order-preserving and compressing transformation semigroups[J]. Journal of Sichuan Normal University(Natural Science), 2014, 37(5):643-648.
[3] XU Bo, ZHAO Ping, LI Junyang. Maximal properties of some subsemigroups of finite order-preserving transformation semigroups[J]. Journal of Math, 2010, 30(4): 617-621.
[4] ZHAO Ping, XU Bo, YANG Mei. A note on maximal properties of some subsemigroups of finite order-preserving transformation semigroups[J]. Communications in Algebra, 2012, 40(3): 1116-1121.
[5] ZHAO Ping, YANG Mei. Maximal properties of some subsemigroups of order-preserving full transformations [J]. Bull. Korean Math, 2013, 50(2): 627-637.
[6] 赵平, 游泰杰, 徐波. 方向保序变换半群K(n,r)的极大正则子半群[J]. 吉林大学学报(理学版), 2011, 49(2):203-206. ZHAO Ping, YOU Taijie, XU Bo. Maximal regular subsemigroups of orientation-preserving transformation semigroups K(n,r)[J]. Journal of Jilin University(Science Edition), 2011, 49(2):203-206.
[7] 赵平, 胡华碧, 徐波. 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]. 山东大学学报(理学版), 2011, 46(12):60-65. ZHAO Ping, HU Huabi, XU Bo. Maximal regular subsemigroups of orientation-preserving or orientation-reserving transformation semigroups I(n,r)[J]. Journal of Shandong University(Natural Science), 2011, 46(12):60-65.
[8] 罗永贵. 半群W(n,r)的非群元秩和相关秩[J]. 山东大学学报(理学版), 2013, 48(12):70-74. LUO Yonggui. Non-group rank and relative rank of the semigroup W(n,r)[J]. Journal of Shandong University(Natural Science), 2013, 48(12):70-74.
[9] GREEN J A. On the structure of semigroups[J]. The Ann of Math, 1951, 54(1): 163-172.
[10] HOWIE J M. Fundamentals of semigroup theory[M]. Oxford: Oxford University Press, 1995.
[11] GANYUSHKIN O, MAZORCHUK V. Classical finite transformation semigroups[M]. London: Springer-Verlag, 2009.
[1] LUO Yong-gui, XU Bo, YOU Tai-jie. On the rank and idempotent rank of each star ideal of the semigroup PHn [J]. J4, 2013, 48(2): 42-48.
[2] LUO Yong-gui. Non-group rank and relative rank of the semigroup W(n,r) [J]. J4, 2013, 48(12): 70-74.
[3] ZHAO Ping. On the idempotent ranks of the semigroup V(n,r) [J]. J4, 2012, 47(2): 78-81.
[4] GAO Rong-hai1,2, XU Bo1. On the rank of order-preserving and compressing singular
transformation semigroups [J]. J4, 2011, 46(6): 4-7.
[5] ZHAO Ping1, YOU Tai-jie2, XU Bo2， HU Hua-bi1. Idempotent rank in decreasing and order-preserving finite partial transformation semigroups [J]. J4, 2011, 46(4): 75-77.
[6] CAO Yong . On the BQ property of linear ordered transformation semigroups [J]. J4, 2008, 43(2): 98-100 .
[7] HAN Hong-xia . Relative ω-compactness in L-order-preserving operator spaces [J]. J4, 2007, 42(7): 91-94 .
[8] CHEN Bin . Cardinal functions in L-fuzzy order-preserving spaces [J]. J4, 2007, 42(12): 116-119 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd