First, we define the pseudo梤ight quasi normal band, at the basic of the defination of the strong band, we get the structure of the pseudo? right quasi normal band.

Shevrin posed an open problem in Reference[1]: are semigroups whose lattice of subsemigroups is complemental periodic? In this paper, it is proved that the openproblem has positive answers for inverse semigroups, rectangular groups and E-right(left) unitary regular semigroups with left(right) normal band.

The existence of a tensor product is proved in the left quasi-normal band category,and the relationship with the tensor product in the semi-group category is provided.