Semigroups of linear transformations with fixed subspaces: Green's relations, ideals and finiteness conditions
Let [Formula: see text] be a vector space and [Formula: see text] denote the semigroup (under the composition of maps) of all linear transformations from [Formula: see text] into itself. For a fixed subspace [Formula: see text] of [Formula: see text] let [Formula: see text] be the subsemigroup of [Formula: see text] consisting of all linear transformations on [Formula: see text] which fix all elements in [Formula: see text] In this paper, we describe Green's relations, regularity and ideals of [Formula: see text] and characterize when [Formula: see text] is factorizable, unit regular and directly finite, from which the results on [Formula: see text] can be recaptured easily when taking [Formula: see text] as a zero subspace of [Formula: see text]
Asian European Journal of Mathematics