Geodesic
Reducibility of semigroups and nilpotent commutators with idempotents of rank two
Ars Mathematica Contemporanea, Tome 3 (2010) no. 1, pp. 99-108.

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Let f be a noncommutative polynomial in two variables. Let S be a multiplicative semigroup of linear operators on a finite-dimensional vector space and T a fixed linear operator such that f(T, S) is nilpotent for all S in 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 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.
DOI : 10.26493/1855-3974.146.279
Keywords: Reducibility, semigroups, commutators, nilpotent operators. 
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Matjaž Omladič; Heydar Radjavi. Reducibility of semigroups and nilpotent commutators with idempotents of rank two. Ars Mathematica Contemporanea, Tome 3 (2010) no. 1, pp. 99-108. doi : 10.26493/1855-3974.146.279. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.146.279/

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