| For each k≥ 2,let Lk denote the semigroup generated by two idempotents E and F subjected to the relation EFEF…=0,where the left side is a product of length k.The semigroup Lk is usually called Lee semigroup.Lee semigroup Lk and its involution（Lk,*）are very important in the study of semigroup varieties and involution semigroup varieties.C.C.Edmunds,E.W.H.Lee,Y.F.Luo and W.T.Zhang have studied the finite basis problem for Lee semigroup Lk,and proved that the Lee semigroup Lk is finitely based if and only if k≤2.As for the involution semigroup（Lk,*）,it is known that（L2:*）and（L3,*）are finitely based and（Lk:*）is non-finitely based for all even k≥ 4.In this paper,we will show that（Lk,*）is non-finitely based for all odd k≥5.Consequently,（Lk,*）is finitely based if and only if k≤3,and thus the finite basis problems for involution Lee semigroups are completely solved. |
