@article{Gao2022, 
author = {Fengxia Gao and Jialei Chen},
title = {Conjugacy classes of left ideals of Sweedler's four-dimensional algebra        H          4},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {5},
pages = {7720-7727},
keywords = {left ideal, idempotent, semigroup, nilpotent left ideal, conjugacy class},
url = {https://www.sciopen.com/article/10.3934/math.2022433},
doi = {10.3934/math.2022433},
abstract = {Let    A be a finite-dimensional algebra with identity over the field        F  ,    U  (  A  ) be the group of units of    A and    L  (  A  ) be the set of left ideals of    A. It is well known that there is an equivalence relation    ∼ on    L  (  A  ) by defining        L    1    ∼      L    2    ∈  L  (  A  ) if and only if there exists some    u  ∈  U  (  A  ) such that        L          1        =      L          2        u.    C  (  A  )  =  {  [  L  ]      |    L  ∈  L  (  A  )  } is the set of equivalence classes determined by the relation    ∼, which is a semigroup with respect to the natural operation    [      L    1    ]  [      L    2    ]  =  [      L    1        L    2    ] for any        L    1    ,      L    2    ∈  L  (  A  ). The purpose of this paper is to describe the structures of semigroup of conjugacy classes of left ideals for the Sweedler's four-dimensional Hopf algebra        H          4      .}
}