### 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

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.

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.
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