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This article is cited in 14 scientific papers (total in 14 papers)
0-dialgebras with bar-unity and nonassociative Rota–Baxter algebras
A. P. Pozhidaev
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
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.
Keywords:
dialgebra, bar-unity, adjoining a bar-unity, Rota–Baxter algebra, enveloping algebra, conformal algebra, alternative dialgebra, variety of dialgebras, unital variety.
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English version:
Siberian Mathematical Journal, 2009, 50:6, 1070–1080
Bibliographic databases:
  
UDC:
512.57
Received: 28.12.2008
Revised: 07.07.2009
Citation:
A. P. Pozhidaev, “0-dialgebras with bar-unity and nonassociative Rota–Baxter algebras”, Sibirsk. Mat. Zh., 50:6 (2009), 1356–1369; Siberian Math. J., 50:6 (2009), 1070–1080
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/smj2055 http://mi.mathnet.ru/eng/smj/v50/i6/p1356
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