01574nab a2200229 i 4500 acta48918 20260224081030.0 170711s2017 hu o 000 eng d 0001 6969 10.14232/actasm-016-319- 1 doi SZTE Egyetemi Kiadványok Repozitórium hun eng Seguins Pazzis Clément de Sums of three quadratic endomorphisms of an infinite-dimensional vector space [elektronikus dokumentum] / Seguins Pazzis Clément de Bolyai Institute, University of Szeged Szeged 2017 83-111 Acta scientiarum mathematicarum 83 No. 1-2 Let V be an infinite-dimensional vector space over a field. In a previous article [5], we have shown tha t every endomorphism of V splits into the sum of four square-zero ones but also into the sum of four idempotent ones. Here, we study decompositions into sums of three endomorphisms with prescribed split annihilating polynomials with degree 2. Except for endomorphisms tha t are the sum of a scalar multiple of the identity and of a finite-rank endomorphism, we achieve a simple characterization of such sums. In particular, we give a simple characterization of the endomorphisms tha t split into the sum of three square-zero ones, and we prove tha t every endomorphism of V is a linear combination of three idempotents. Természettudományok Matematika Matematika http://acta.bibl.u-szeged.hu/48918/1/math_083_numb_001-002_083-111.pdf Dokumentum-elérés