Reducibility of semigroups and nilpotent commutators with idempotents of rank two - Omladič, Matjaž (Ars mathematica contemporanea, 2010)
Let ?$f$? be a noncommutative polynomial in two variables. Let ?$\mathcal{S}$? be a multiplicative semigroup of linear operators on a finite-dimensional vectorspace and ?$T$? a fixed linear operator such that ?$f(T, S)$? is nilpotent for all ?$S$? in ?$\mathcal{S}$?. In H. Radjavi, M. Omladič, Nilpotent commutators and reducibility of semigroups, Lin. and Multilin. Alg. 57 (2009), 307-317 the authors proposed questions, what one can say about the invariant subspace structure of ?$\mathcal{S}$? under this and other related conditions. In particular, they study the question under the condition that ?$S, T^2 = 0$?, where ?$T$? is a given idempotent of rank one. In this paper we extend some of the results given there to the case that ?$T$? is a given idempotent of rank two.
Keywords: linearna algebra; matematika