JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (10): 63-70.doi: 10.6040/j.issn.1671-9352.0.2019.922

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Rank and relative rank of the semigroup PD(n,r)

ZHANG Qian-tao, LUO Yong-gui*, ZHAO Ping   

  1. School of Mathematics Science, Guizhou Normal University, Guiyang 550025, Guizhou, China
  • Online:2020-10-20 Published:2020-10-07

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Abstract: Let PDn be the semigroup of all distance-preserving partial one-to-one singular transformations on a finite-chain ［n］(n≥3), and let PD(n,r)={α∈PDn:|im(α)|≤r}(0≤r≤n-1)be the two-sided ideal of the semigroup PDn. By analyzing the elements with rank r of the semigroup PDn, the minimal generating set and rank of the semigroup PD(n,r)are obtained. Furthermore, the relative rank of the semigroup PD(n,r)with respect to its ideal PD(n,l)is determined for 0≤l≤r.

Key words: distance-preserving, partial one-to-one singular transformation semigroup, generating set, rank, relative rank

CLC Number: 

  • O152.7
[1] 罗永贵,游泰杰,高荣海.关于OIn和DOIn的理想的生成集及其秩[J].贵州师范大学学报(自然科学版),2012,40(2):7-10. LUO Yonggui, YOU Taijie, GAO Ronghai. Systems of generators and ranks of ideals of OIn and DOIn [J]. Journal of Guizhou Normal University(Natural Sciences), 2012, 40(2):7-10.
[2] 罗永贵.半群DOn中理想的秩和相关秩[J].吉林大学学报(理学版),2013,51(1):69-73. LUO Yonggui. Rank and relative rank of each ideal of the semigroup DOn[J]. Journal of Jilin University(Science Edition), 2013, 51(1):69-73.
[3] 李晓敏,罗永贵,赵平.半群OPD(n,r)的秩和相关秩[J].四川师范大学学报(自然科学版),2019,42(6):770-778. LI Xiaomin, LUO Yonggui, ZHAO Ping. Rank and relative rank of the semigroup OPD(n,r)[J]. Journal of Sichuan Normal University(Natural Science), 2019, 42(6):770-778.
[4] 罗永贵,徐波,游泰杰.半群CDOn的每个星理想秩和相关秩[J].数学的实践与认识,2015,45(12):240-245. LUO Yonggui, XU Bo, YOU Taijie. Rank and relative rank of rach star ideal of the semigroup CDOn[J]. Journal of Mathematics in Practice and Theory, 2015, 45(12):240-245.
[5] 罗永贵.半群CSPOn中星理想的秩和相关秩[J].数学的实践与认识,2018,48(6):222-230. LUO Yonggui. On the rank and relative rank of rach star ideal of the semigroup DOn[J]. Journal of Mathematics in Practice and Theory, 2018, 48(06):222-230.
[6] 赵平,徐波,游泰杰.半群CPOn的秩[J].西南大学学报(自然科学版),2011,33(6):106-110. ZHAO Ping, XU Bo, YOU Taijie. Rank of the semigroup CPOn[J]. Journal of Southwest University(Natural Science Edition), 2011, 33(6):106-110.
[7] 罗永贵,徐波,高荣海.半群CPOn的每个星理想的秩和相关秩[J].西南大学学报(自然科学版),2013,35(8):77-82. LUO Yonggui, XU Bo, GAO Ronghai. On the rank and relative rank of each star ideal of the semigroup CPOn[J]. Journal of Southwest University(Natural Science Edition), 2013, 35(8):77-82.
[8] 高荣海,徐波.关于保序压缩奇异变换半群的秩[J].山东大学学报(理学版),2011,46(6):4-7. GAO Ronghai, XU Bo. On the rank of order-preserving and compressing singular transformation semigroup [J]. Journal of Shandong University(Natural Science), 2011, 46(6):4-7.
[9] 罗永贵,徐波,游泰杰.半群Hn的每个星理想秩和幂等元秩[J].四川师范大学学报(自然科学版),2014,37(1):58-61. LUO Yonggui, XU Bo, YOU Taijie. On the rank and idempotent rank of each star ideal of the semigroup Hn[J]. Journal of Sichuan Normal University(Natural Science), 2014, 37(1):58-61.
[10] 罗永贵,杨丛丽.U(n,r)的秩和拟幂等元秩[J].四川师范大学学报(自然科学版),2015,38(4):508-513. LUO Yonggui, YANG Congli. On the rank and quasi-idempotent rank of the semigroup U(n,r)[J]. Journal of Sichuan Normal University(Natural Science), 2015, 38(4):508-513.
[11] 龙伟峰,徐波,游泰杰.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. LONG Weifeng, XU Bo, YOU Taijie. The rank of the semigroup of E-preserving and strictly order-preserving partial one-one transformations[J]. Journal of Sichuan Normal University(Natural Science), 2014, 37(3):316-319.
[12] HOWIE J M, RUŬKUC N, HIGGINS P M. On relative ranks of full transformation semigroups [J].Communication in Algebra, 1998, 26(3):733-748.
[13] GANYUSHKIN O, MAZORCHUK V. Classical finite transformation semigroups[M]. London: Springer-Verlag, 2009.
[14] HOWIE J M. Fundamentals of semigroup theory[M]. Oxford: Oxford University Press, 1995.
[15] FOUNTAIN J B. Abundant semigroups[J]. Proceedings of the London Mathematical Society, 1982, 44(3):103-129.
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