Möbius type semigroups in \(SL(2,F)\) (Q1806056)

In this paper the authors extend known results about semigroups in SL\((2,{\mathbb R})\) to SL\((2,F)\) for \(F\) an ordered field by showing that each element of the subsemigroup \(S\) of SL\((2,F)\) having all entries non-negative admits a unique triple decomposition as a product of an upper triangular, a diagonal, and a lower triangular matrix. Furthermore, it is shown that the semigroup \(\pm S\) is a maximal subsemigroup of SL\((2,F)\).