Some Studies On Conjugacy Relations In Semigroups

The main content researched in this thesis is the conjugacy relations in several classes of semigroups.Firstly,p-conjugacy in regular -semigroups and cancellative semigroups are investigated,and the structure theorem for regular -semigroups given by Koˇcin,Munn and Reilly is used to prove the transitivity of p-conjugacy in such semigroups.By a specific analysis of examples in the literature,it is shown that the p-conjugacy in a cancellative semigroup that is embeddable in a group is not necessarily transitive.Secondly,the o-conjugacy in -inversive semigroups is discussed,and some necessary or sufficient conditions under which o-conjugacy is universal relation or congruence relations are given.Thirdly,some properties of re-conjugacy in restriction semigroups are explored,and the reltionship between re-conjugacy and n-conjugacy is considered.The above work have answered some problems on conjugacy relations in semigroups proposed by related scholars.Finally,the p-conjugacy and n-conjugacy in graph inverse semigroups are considered and their specific descriptions are given.