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oai:riuma.uma.es:10630/265062026-02-03T10:50:34Zcom_10630_2254col_10630_37953

00925njm 22002777a 4500 dc Cabrera-Casado, Yolanda author Martín-Barquero, Dolores author Martín-González, Cándido author Tocino-Sánchez, Alicia author 2022-12-28 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. 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 Productos tensoriales Álgebras genéticas Algebras no asociativas Tensor Product of Evolution Algebras