2026-05-28T11:27:46Zhttps://riuma.uma.es/rest/oai/request
oai:riuma.uma.es:10630/460282026-03-13T00:46:12Zcom_10630_2254col_10630_37953
RIUMA. Repositorio Institucional de la Universidad de Málaga author Cabrera-Casado, Yolanda author Gonçalves, Daniel author Martín Barquero, Dolores author Martín González, Cándido author Ruiz Campos, Iván 2026-03-12T13:15:32Z 2026-03-09 Cabrera Casado, Y., Cardoso Gonçalves, M. I., Gonçalves, D., Martín Barquero, D., Martín González, C., & Ruiz Campos, I. (2026). Centroid and algebraic properties of evolution algebras through graphs. Linear Algebra and Its Applications, 738, 243–268. https://doi.org/10.1016/j.laa.2026.03.006 https://hdl.handle.net/10630/46028 10.1016/j.laa.2026.03.006 The leitmotiv of this paper is linking algebraic properties of an evolution algebra with combinatorial properties of the (possibly several) graphs that one can associate to the algebra. We link nondegeneracy, zero annihilator, absorption property, von Neumann regularity and primeness with suitable properties in the associated graph. In the presence of semiprimeness, the property of primeness is equivalent to any associated graph being downward directed. We also provide a description of the prime ideals in an evolution algebra and prove that certain algebraic properties, such as semiprimeness and perfection, can not be characterized in combinatorial terms. We describe the centroid of evolution algebras as constant functions along the connected components of its associated graph. The dimension of the centroid of a zero annihilator algebra A agrees with the cardinal of the connected components of any possible graph associated to A. This is the combinatorial expression of an algebraic uniqueness property in the decomposition of A as indecomposable algebras with 1-dimensional centroid. eng Attribution 4.0 International Von Neumann, Algebras de Álgebra Centroid and algebraic properties of evolution algebras through graphs journal article 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 URL https://riuma.uma.es/bitstreams/8de56f8c-55a3-4756-8971-5552ef64b7c4/download File MD5 47f7dccc7eb454e2d65192f52696cda4 1051473 application/pdf cENTROID.pdf