Maximal (completely) isolated subsemigroups of semigroup BI(n,r)

Abstract

Abstract: Let I_n and S_n be symmetric inverse semigroup and symmetric group on the finite set X_n={1,2,…,n}, respectively. For 0≤r≤n－1, put I(n,r)={α∈I_n:|im(α)|≤r}, then the I(n,r) is a two-sided ideals of symmetric inverse semigroup I_n. Denote B_n=〈δ_n〉, where there is i δ_n=n+1－i for any i∈X_n, saying that B_n is a circle group on X_n. By analyzing the Green’s relation and generative relation of the semigroup BI(n,r)=I(n,r)∪B_n, the complete classification of the (completely) isolated subsemigroups of BI(n,r) is obtained. Furthermore, the coincide of maximal isolated subsemigroups and maximal completely isolated subsemigroups of BI(n,r) be proved.

Key words: symmetric inverse semigroup, symmetric group, circle group, (compeletly) isolated subsemigroups, the maximal (completely) isolated subsemigroups

CLC Number:

O152.7

LUO Yong-gui, XIAO Jian, YU Jiang-hui. Maximal (completely) isolated subsemigroups of semigroup BI(n,r)[J]. Journal of Lanzhou University of Technology, 2025, 51(3): 156-160.

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: https://journal.lut.edu.cn/EN/

https://journal.lut.edu.cn/EN/Y2025/V51/I3/156

References

[1] GANYUSHKIN A G,MAZORCHUK V S.Structure of subsemigroups of factor-powers of finite symmetric groups[J].Mathematical Notes,1995,58(3):910-920.
[2] TSYAPUTA G.Isolated and nilpotent subsemigroups in the variants of IS_n[J].Algebra and Discrete Mathematics,2006,5(1):79-89.
[3] MAZORCHUK V,TSYAPUTA G.Isolated subsemigroups in the variants of T_n[J].Acta Mathematica Universitais Comenianae,2008,77(1):63-84.
[4] KORKMAZ E,AYIK H.Isolated subsemigroups of order-preserving and decreasing transformation semigroups[J].Bulletin of the Malaysian Mathematical Sciences Society,2022,45:663-675.
[5] 田振际,马存德.π-正则半群的全π-正则子半群格[D].兰州:兰州理工大学,2020.
[6] 王永铎,徐鹏.广义D4模[J].兰州理工大学学报,2022,48(6):145-148.
[7] 袁月,赵平.半群H_(n,m)的独立子半群[J].西南大学学报(自然科学版),2021,43(6):74-81.
[8] ZHAO P,HU H B.Locally maximal regular subsemibands of the finite transformation semigroups T(n,r)[J].Semigroup Forum,2019,98(1):172-183.
[9] 袁月,赵平.半群H^*_(n,m)(r)的极大子半群与极大正则子半群[J].山东大学学报(理学版),2020,55(12):19-24.
[10] 邵海琴,梁茂林,董芳芳.半环同态的若干性质[J].兰州理工大学学报,2022,48(5):161-165.
[11] 胡华碧,赵平.半群T(n,r)的极大(正则)子半群的完全分类[J].西南师范大学学报(自然科学版),2021,46(6):5-8.
[12] 金久林,腾文,祝富洋,等.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.
[13] 李亚雷,徐波,戴先胜.半群PCS_n的极大子半群[J].数学的实践与认识,2019,49(10):303-307.
[14] 金久林,游泰杰,徐波.有限全变换半群变种具有某种性质的极大子半群[J].吉林大学学报(理学版),2018,56(3):549-555.
[15] HOWIE J M.Fundamentals of semigroup theory[M].Oxford:Oxford University Press,1995.
[16] GANYUSHKIN O,MAZORCHUK V.Classical finite transformation semigroups[M].London:Springer-Verlag,2009.