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Cabrera-Casado, Yolanda Martín-Barquero, Dolores Martín-González, Cándido Tocino-Sánchez, Alicia 2023-05-08T08:42:06Z 2023-05-08T08:42:06Z 2022-12-28 Cabrera Casado, Y., Martín Barquero, D., Martín González, C. et al. Tensor Product of Evolution Algebras. Mediterr. J. Math. 20, 43 (2023). https://doi.org/10.1007/s00009-022-02246-5 https://hdl.handle.net/10630/26506 10.1007/s00009-022-02246-5 The starting point of this work is the fact that the class of evolution algebras over a fixed field is closed under tensor product. We prove that, under certain conditions, the tensor product is an evolution algebra if and only if every factor is an evolution algebra. Another issue arises about the inheritance of properties from the tensor product to the factors and conversely. For instance, nondegeneracy, irreducibility, perfectness and simplicity are investigated. The four-dimensional case is illustrative and useful to contrast conjectures, so we achieve a complete classification of four-dimensional perfect evolution algebras emerging as tensor product of two-dimensional ones. We find that there are four-dimensional evolution algebras that are the tensor product of two nonevolution algebras. eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Productos tensoriales Álgebras genéticas Algebras no asociativas Tensor Product of Evolution Algebras journal article