Products of nilpotent linear transformations
Robert Patrick Sullivan · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1994
In this paper we characterise the linear transformations of an infinite-dimensional vector space that can be written as the product of nilpotent transformations. This and a linear version of Malcev's congruence on transformation semigroups are then used to construct a new class of congruence-free semigroups.