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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 6, Pages 1237–1250 (Mi smj2158)  
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
Full-text PDF (358 kB) Citations (27)
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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
English version:
Siberian Mathematical Journal, 2010, Volume 51, Issue 6, Pages 978–988
DOI: https://doi.org/10.1007/s11202-010-0097-1
Bibliographic databases:
Document Type: Article
UDC: 510.53+512.552.4+512.579+519.117
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 27 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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