RT Journal Article
T1 Centroid and algebraic properties of evolution algebras through graphs
A1 Cabrera-Casado, Yolanda
A1 Gonçalves, Daniel
A1 Martín Barquero, Dolores
A1 Martín González, Cándido
A1 Ruiz Campos, Iván
K1 Von Neumann, Algebras de
K1 Álgebra
AB 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.
PB Elsevier
YR 2026
FD 2026-03-09
LK https://hdl.handle.net/10630/46028
UL https://hdl.handle.net/10630/46028
LA eng
NO 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
NO Funding for open access charge: Universidad de Málaga / CBUA.
NO Ministerio de Ciencia e Innovación
NO Junta de Andalucía
NO Comunidad Autónoma de La Rioja
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 21 mar 2026