Kozybaev, D. Kh.; Umirbaev, U. U. The Magnus embedding for right-symmetric algebras. (Russian, English) Zbl 1059.17001 Sib. Mat. Zh. 45, No. 3, 592-599 (2004); translation in Sib. Math. J. 45, No. 3, 488-494 (2004). An algebra \(A\) is called right-symmetric if the identity \((xy)z-x(yz)=(xz)y-x(zy)\) holds for all \(x,y,z\in A\). Let \(A\) be a right-symmetric algebra and let \(U(A)\) be the universal multiplicative enveloping algebra of \(A \big(U(A)\) is an associative algebra with unity which is generated by the operators of left and right multiplication\(\big)\). The authors find a linear basis of \(U(A)\) starting from a linear basis of \(A\). An analog of the Magnus embedding for right-symmetric algebras is also proven. Reviewer: A. P. Pozhidaev (Novosibirsk) Cited in 3 Documents MSC: 17A30 Nonassociative algebras satisfying other identities Keywords:right-symmetric algebra; Magnus embedding; universal enveloping algebra PDFBibTeX XMLCite \textit{D. Kh. Kozybaev} and \textit{U. U. Umirbaev}, Sib. Mat. Zh. 45, No. 3, 592--599 (2004; Zbl 1059.17001); translation in Sib. Math. J. 45, No. 3, 488--494 (2004) Full Text: EuDML EMIS