Abstract
We describe all homogeneous structures of Rota-Baxter algebras on a 0-dialgebra with associative bar-unity and give a corollary on the structure of a Rota-Baxter algebra on an arbitrary associative dialgebra with bar-unity as well as a unital associative conformal algebra. We prove that an arbitrary alternative dialgebra may be embedded into an alternative dialgebra with associative barunity. We suggest the definition of variety of dialgebras in the sense of Eilenberg which is equivalent to that introduced earlier by Kolesnikov.
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Original Russian Text Copyright © 2009 Pozhidaev A. P.
The author was supported by the Russian Foundation for Basic Research (Grant 09-01-00157), the FAPESP (2008/50142-8), the Integration Grant of the Siberian Division of the Russian Academy of Sciences (No. 97), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-344.2008.1), and the Program “Development of the Scientific Potential of Higher School” of the Russian Federal Agency for Education (Grant 2.1.1.419).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 6, pp. 1356–1369, November–December, 2009.
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Pozhidaev, A.P. 0-dialgebras with bar-unity and nonassociative Rota-Baxter algebras. Sib Math J 50, 1070–1080 (2009). https://doi.org/10.1007/s11202-009-0118-0
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DOI: https://doi.org/10.1007/s11202-009-0118-0