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Sibirsk. Mat. Zh., 2010, Volume 51, Number 6, Pages 1237–1250 (Mi smj2158)  

This article is cited in 15 scientific papers (total in 15 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.

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English version:
Siberian Mathematical Journal, 2010, 51:6, 978–988

Bibliographic databases:

Document Type: Article
UDC: 510.53+512.552.4+512.579+519.117
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

Citation in format AMSBIB
\by L.~A.~Bokut, Yu.~Chen, X.~Deng
\paper Gr\"obner--Shirshov bases for Rota--Baxter algebras
\jour Sibirsk. Mat. Zh.
\yr 2010
\vol 51
\issue 6
\pages 1237--1250
\jour Siberian Math. J.
\yr 2010
\vol 51
\issue 6
\pages 978--988

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    This publication is cited in the following articles:
    1. Chen Yu., Mo Q., “Embedding dendriform algebra into its universal enveloping Rota-Baxter algebra”, Proc. Amer. Math. Soc., 139:12 (2011), 4207–4216  crossref  mathscinet  zmath  isi  elib  scopus
    2. Bokut L.A., Chen Yu., Chen Y., “Grobner-Shirshov bases for Lie algebras over a commutative algebra”, J. Algebra, 337:1 (2011), 82–102  crossref  mathscinet  zmath  isi  elib  scopus
    3. Gubarev V.Yu., Kolesnikov P.S., “Embedding of Dendriform Algebras Into Rota-Baxter Algebras”, Cent. Eur. J. Math., 11:2 (2013), 226–245  crossref  mathscinet  zmath  isi  elib  scopus
    4. Leonid A. Bokut, Yuqun Chen, “Gröbner–Shirshov bases and PBW theorems”, Zhurn. SFU. Ser. Matem. i fiz., 6:4 (2013), 417–427  mathnet
    5. Bremner M.R., Madariaga S., “Special Identities for the Pre-Jordan Product in the Free Dendriform Algebra”, Linear Alg. Appl., 439:2 (2013), 435–454  crossref  mathscinet  zmath  isi  elib  scopus
    6. Bokut L.A., Chen Yu., Mo Q., “Grobner-Shirshov Bases for Semirings”, J. Algebra, 385 (2013), 47–63  crossref  mathscinet  zmath  isi  elib  scopus
    7. Gao X., Guo L., Zheng Sh., “Construction of Free Commutative Integro-Differential Algebras by the Method of Grobner-Shirshov Bases”, J. Algebra. Appl., 13:5 (2014), 1350160  crossref  mathscinet  zmath  isi  elib  scopus
    8. Bokut L.A., Chen Yu., “Grobner-Shirshov Bases and Their Calculation”, Bull. Math. Sci., 4:3 (2014), 325–395  crossref  mathscinet  zmath  isi  elib  scopus
    9. Gao X., Guo L., “Constructions of Free Commutative Integro-Differential Algebras”, Algebraic and Algorithmic Aspects of Differential and Integral Operators, Lecture Notes in Computer Science, 8372, eds. Barkatou M., Cluzeau T., Regensburger G., Rosenkranz M., Springer-Verlag Berlin, 2014, 1–22  crossref  mathscinet  zmath  isi
    10. Gao X., Guo L., Rosenkranz M., “Free Integro-Differential Algebras and Grobner Shirshov Bases”, J. Algebra, 442:SI (2015), 354–396  crossref  mathscinet  zmath  isi  elib  scopus
    11. Zheng Sh., Guo L., “Relative Locations of Subwords in Free Operated Semigroups and Motzkin Words”, Front. Math. China, 10:5 (2015), 1243–1261  crossref  mathscinet  zmath  isi  elib  scopus
    12. Bokut L.A., Chen Yu., Chen W., Li J., “New Approaches To Plactic Monoid Via Grobner-Shirshov Bases”, J. Algebra, 423 (2015), 301–317  crossref  mathscinet  zmath  isi  elib  scopus
    13. V. Yu. Gubarev, “Free Lie Rota–Baxter algebras”, Siberian Math. J., 57:5 (2016), 809–818  mathnet  crossref  crossref  isi  elib  elib
    14. Li Yu., Mo Q., “Embedding Into 2-Generated Simple Associative (Lie) Algebras”, Commun. Algebr., 45:6 (2017), 2435–2443  crossref  mathscinet  zmath  isi  scopus
    15. Yu. Chen, Y. Li, Q. Tang, “Gröbner–Shirshov bases for some Lie algebras”, Siberian Math. J., 58:1 (2017), 176–182  mathnet  crossref  crossref  isi  elib  elib
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