García, EstherGómez Lozano, MiguelMuñoz Alcázar, RubénVera de Salas, Guillermo2023-09-222023-09-222022Esther García, Miguel Gómez Lozano, Rubén Muñoz Alcázar, Guillermo Vera de Salas, Gradings induced by nilpotent elements, Linear Algebra and its Applications, Volume 656, 2023, Pages 92-111, ISSN 0024-3795, https://doi.org/10.1016/j.laa.2022.09.0170024-3795https://hdl.handle.net/10115/24475The authors express their sincere thanks to the anonymous expert referee for the careful reading of the manuscript and his/her competent and insightful comments and suggestions.An element a is nilpotent last-regular if it is nilpotent and its last nonzero power is von Neumann regular. In this paper we show that any nilpotent last-regular element a in an associative algebra R over a ring of scalars Φ gives rise to a complete system of orthogonal idempotents that induces a finite Z-grading on R; we also show that such element gives rise to an sl2-triple in R with semisimple adjoint map adh, and that the grading of R with respect to the complete system of orthogonal idempotents is a refinement of the Φgrading induced by the eigenspaces of adh. These results can be adapted to nilpotent elements a with all their powers von Neumann regular, in which case the element a can be completed to an sl2-triple and a is homogeneous of degree 2 both in the Z-grading of R and in the Φ-grading given by the eigenspaces of adh.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/von Neumann regularNilpotent elementGradingsl2-tripleinfo:eu-repo/semantics/article10.1016/j.laa.2022.09.017info:eu-repo/semantics/openAccess