The finite basis property of a certain semigroup of upper triangular matrices over a field

摘要

Let UTn(F) be the semigroup of all upper triangular nxn matrices over a field F whose main diagonal entries are 0s and/or 1s. Volkov proved that UT3(R) is nonfinitely based as both a plain semigroup and an involution semigroup under the reflection with respect to the secondary diagonal. In this paper, we shall prove that UT2(F) is finitely based for any field F. When F = R, this result partially answers an open question posed by Volkov.