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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 6, Pages 1237–1250
(Mi smj2158)
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This article is cited in 27 scientific papers (total in 27 papers)
Gröbner–Shirshov bases for Rota–Baxter algebras
L. A. Bokutab, Yu. Chenb, X. Dengb a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b South China Normal University, Guangzhou, Republic of China
Abstract:
We establish the composition-diamond lemma for associative nonunitary Rota–Baxter algebras of weight $\lambda$. To give an application, we construct a linear basis for a free commutative and nonunitary Rota–Baxter algebra, show that every countably generated Rota–Baxter algebra of weight 0 can be embedded into a two-generated Rota–Baxter algebra, and prove the 1-PBW theorems for dendriform dialgebras and trialgebras.
Keywords:
Rota–Baxter algebra, Gröbner–Shirshov basis.
Received: 15.09.2009
Citation:
L. A. Bokut, Yu. Chen, X. Deng, “Gröbner–Shirshov bases for Rota–Baxter algebras”, Sibirsk. Mat. Zh., 51:6 (2010), 1237–1250; Siberian Math. J., 51:6 (2010), 978–988
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https://www.mathnet.ru/eng/smj2158 https://www.mathnet.ru/eng/smj/v51/i6/p1237
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Abstract page: | 442 | Full-text PDF : | 163 | References: | 50 | First page: | 2 |
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