The Finite Bases Problem For Involution Semigroups(BU_n,*)

Let?BU_n,*?is all boolean upper triangular n×n matrices with 1's on the main diagonal under Matrix multiplication and reflection with respect to the secondary diago-nal.In this paper,it is shown that some identities and properties the involution monoid?BU₃,*?satisfied;it is shown that the involution monoid?BU_n,*?is nonfinitely based when n?5.Some identities and properties it satisfied are given.