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oai:riuma.uma.es:10630/460282026-03-13T00:46:12Zcom_10630_2254col_10630_37953

Centroid and algebraic properties of evolution algebras through graphs Cabrera-Casado, Yolanda Gonçalves, Daniel Martín Barquero, Dolores Martín González, Cándido Ruiz Campos, Iván Von Neumann, Algebras de Álgebra 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. 2026-03-09 journal article 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 eng http://creativecommons.org/licenses/by/4.0/ open access Attribution 4.0 International Elsevier