The Finite Bases Problem For Semigroups Of Triangular Boolean Matrices

Let(TB_n,^*)be the involution semigroup of all upper triangular booleann×nmatrices,where^*denotes the reflection with respect to the secondary diagonal.It is shown by K.Auinger et al.that(TB_n,^*)is inherently non-finitely based if n?3,but the case when n=2 remained open.In this paper,we study the finite basis problem for the the involution semigroup?TB₂,^*?.We give a sufficient condition under which an involution semigroup is non-finitely based.As an application,it is shown that?TB₂,^*?is non-finitely based.Then we completely determine the finite basis problem of involution semigroup(TB_n,^*).