0 KB167 KB26 KB200820252010Omladič, MatjažRadjavi, Heydarštevilka:1letnik:3str. 99-108COBISSID:15563865ISSN:1855-3966URN:URN:NBN:SI:doc-YOAYKNLXenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporanealinearna algebramatematikaReducibility of semigroups and nilpotent commutators with idempotents of rank two|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 twoNaj bo ?$f$? nekomutativni polinom v dveh spremenljivkah. Naj bo ?$\mathcal{S}$? multiplikativna polgrupa linearnih operatorjev na končnorazsežnem vektorkskem prostoru in ?$T$? tak linearen operator, da je ?$f(T, S)$? nilpotenten za vsak ?$S$? v ?$\mathcal{S}$?. V članku H. Radjavi, M. Omladič, Nilpotent commutators and reducibility of semigroups, Lin. and Multilin. Alg. 57 (2009), 307-317 sta avtorja zastavila vprašanje, kaj lahko povemo o strukturi invariantnih podprostorov polgrupe ?$\mathcal{S}$? pod tem in nekaterimi sorodnimi pogoji. V posebnem sta študirala vprašanje pod pogojem, da je ?$S, T^2 = 0$?, kjer je ?$T$? dan idempotent ranga ena. V članku posplošimo ta rezultat na primer, koje ?$T$? idempotent ranga dvaTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije