81 citations · 453 across the 60 of their papers we have counts for
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Composition-Diamond Lemma for Non-associative Algebras over a Commutative Algebra
Yuqun Chen, Jing Li, Mingjun Zeng
We establish the Composition-Diamond lemma for non-associative algebras over a free commutative algebra. As an application, we prove that every countably generated non-associative…
Gröbner-Shirshov Bases and Hilbert Series of Free Dendriform Algebras
Yuqun Chen, Bin Wang
In this paper, we give a Gröbner-Shirshov basis of the free dendriform algebra as a quotient algebra of an -algebra. As applications, we obtain a normal form of the free dendrif…
Gröbner-Shirshov bases for Lie algebras over a commutative algebra
L. A. Bokut, Yuqun Chen, Yongshan Chen
In this paper we establish a Gröbner-Shirshov bases theory for Lie algebras over commutative rings. As applications we give some new examples of special Lie algebras (those embedda…
Embedding dendriform dialgebra into its universal enveloping Rota-Baxter algebra
Yuqun Chen, Qiuhui Mo
In this paper, by using Gröbner-Shirshov bases for Rota-Baxter algebras, we prove that every dendriform dialgebra over a field of characteristic 0 can be embedded into its universa…
Gröbner-Shirshov bases for -algebras
L. A. Bokut, Yuqun Chen, Jiapeng Huang
In this paper, we firstly establish Composition-Diamond lemma for -algebras. We give a Gröbner-Shirshov basis of the free -algebra as a quotient algebra of a free -algebra…