Skew idempotents in linear transformation semigroups
Tawhat Changphas, Robert Patrick Sullivan · Linear and Multilinear Algebra · 2009
If S is a regular semigroup, then (e, f) is a skew pair of idempotents in S if e, f and fe are idempotent, but ef is not. In 2006, Blyth and Almeida Santos determined when four types of such skew pairs exist in T(X), the total transformation semigroup on a set X. Here we do the same for the semigroup T(V) consisting of all linear transformations of a vector space V.