JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (3): 14-18.doi: 10.6040/j.issn.1671-9352.0.2022.223

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The structure of proper glrac semigroups

LIU Hai-jun1,2, GUO Xiao-jiang1*   

  1. 1. School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022, Jiangxi, China;
    2. School of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, Guangdong, China
  • Online:2023-03-20 Published:2023-03-02

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Abstract: The concept of glrac semigroupoids is introduced and a structure theorem of proper glrac semigroups is established by means of the action of a monoid upon a proper glrac semigroupoid on the left. As an application, the construction of proper left GC-lpp semigroups is also considered.

Key words: glrac semigroups, semigroupoids, monoids

CLC Number: 

  • O152.7
[1] BRANCO M J J, GOMES G M S, GOULD V. Extensions and covers for semigroups whose idempotents form a left regular band [J]. Semigroup Forum, 2010, 81:51-70.
[2] FOUNTAIN J B. Adequate semigroups[J]. Proc Edinb Math Soc, 1979, 22(2):113-125.
[3] FOUNTAIN J B. Abundant semigroups[J]. Proc Edinb Math Soc, 1982, 44(3):103-129.
[4] FOUNTAIN J B, GOMES G M S. Proper covers of ample monoids [J]. Proc Edinb Math Soc, 2006, 49:277-289.
[5] GUO Xiaojiang. Abundant left GC-lpp semigroups[J]. Southeast Asian Bull Math, 2000, 24:41-50.
[6] GUO Xiaojiang, GUO Yuqi, SHUM Karping. Left abundant semigroups[J]. Comm Algebra, 2004, 32:2061-2085.
[7] LIU Yanhong, GUO Junying, GUO Xiaojiang. Almost factorizable glrac semigroups[J]. Bull Malays Math Sci Soc, 2022, 45:273-305.
[8] LIU Haijun, GUO Xiaojiang. Congruences on glrac semigroups(I)[J/OL]. J Algebra Appl, https://doi.org/10.1142/S0219498822502401.
[9] GUO Junying, GUO Xiaojiang, LIU Haijun, et al. Proper covers for glrac semigroups[EB/OL].[2021-12-01]. https://ef.msp.org/submin_new.php?j=ak_pmh
[10] GUO Xiaojiang, DING Chuanmei, GUO Junying. GLRAC semigroups[EB/OL]. [2022-01-15]. https://www.degruyter.com/journal/key/math/html
[11] HOWIE J M. Fundamentals of semigroup theory[M]. Oxford: Clarendon Press, 1995.
[12] GOULD V. Notes on restriction semigroups and related structures formerly(weakly)left E-ample semigroups[EB/OL]. [2021-09-10] https://www.researchgate.net/publication/237604491.
[13] ZHANG Zhiqin, GUO Junying, GUO Xiaojiang. Congruence-free restriction semigroups [J]. Italian Journal of Pure and Applied Mathematics[EB/OL]. [2022-01-20]. https://ijpam.uniud.it/journal/home.html
[14] HOLLING C D. From right PP monoids to restriction semigroups: a survey [J]. European J Pure Appl Math, 2009, 2:21-57.
[15] SZENDREI M B. Embedding into almost left factorizable restriction semigroups [J]. Comm Algebra, 2013, 41:1458-1483.
[16] 李春华,徐保根,黄华伟. 真弱左型B-半群上的幂单同余[J]. 山东大学学报(理学版), 2016, 51(8):49-52. LI Chunhua, XU Baogen, HUANG Huawei. Unipotent congruences on a proper weakly left type B semigroup[J]. Journal of Shandong University(Natural Science), 2016, 51(8):49-52.
[17] 晏潘, 严庆富, 王守峰. P-限制半群的λ-半直积[J]. 山东大学学报(理学版),2020,55(4):13-20. YAN Pan, YAN Qingfu, WANG Shoufeng. λ-semidirect products of P-restriction semigroups[J]. Journal of Shandong University(Natural Science), 2020, 55(4):13-20.
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