Cedilnik, A. Subassociative algebras. (English) Zbl 1014.17002 Acta Math. Univ. Comen., New Ser. 66, No. 2, 229-241 (1997). Summary: An algebra is subassociative if the associator \([x, y, z]\) of any three elements \(x, y, z\) is their linear combination. In this paper we prove that any such algebra is Lie-admissible and that almost any such algebra is proper in the sense that there exists an invariant bilinear form \(A\) for which there holds the following identity: \([x, y, z] = A(y, z)x-A(x,y)z\) which enables a close connection with associative algebras. We discuss also the improper subassociative algebras. Cited in 1 Document MSC: 17A30 Nonassociative algebras satisfying other identities 17D25 Lie-admissible algebras Keywords:invariant bilinear form; associator PDFBibTeX XMLCite \textit{A. Cedilnik}, Acta Math. Univ. Comen., New Ser. 66, No. 2, 229--241 (1997; Zbl 1014.17002) Full Text: EuDML EMIS