THE FINITE BASIS PROBLEM FOR INVOLUTION SEMIGROUPS OF TRIANGULAR $2imes 2$ MATRICES

摘要

Let Tn(F) be the semigroup of all upper triangular n n matrices over a field F. Let UTn(F) and UT 1 n (F) be subsemigroups of Tn(F), respectively, having 0s and /or 1s on the main diagonal and 0s and /or 1s on the main diagonal. We give some su fficient conditions under which an involution semigroup is nonfinitely based. As an application, we show that UT2(F); UT 1 2 (F) and T2(F) as involution semigroups under the skew transposition are nonfinitely based for any field F.