@UNPUBLISHED{publication1, title = "Decompositions of linear spaces induced by n-linear maps", author = "{CALDER{\'{O}}N, Antonio J.} and {KAYGORODOV, Ivan} and {SARAIVA, Paulo}", year = "2018-01-24", abstract = " Let V be an arbitrary linear space and f : V \× ... \× V \→ V an n-linear map. We show that, for any choice of basis B of V, the n-linear map f induces on V a decomposition (depending on B) V = \⊕Vj as a direct sum of linear subspaces, which is f-orthogonal in the sense f(V,...,Vj,...,Vk,...,V) = 0 when j $\backslash$neq k, and in such a way that any Vj is strongly f-invariant in the sense f(V,...,Vj,...,V) \⊂ Vj. We also characterize the f-simplicity of any Vj. Finally, an application to the structure theory of arbitrary n-ary algebras is also provided. It is the full generalization of some early result [6]. ", url = "http://www.mat.uc.pt/preprints/eng\_2018.html", note = "" }