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L.A. Bokut

  1. Gr\"obner-Shirshov bases for Rota-Baxter algebras.

    Tue, 08/18/2009 - 11:53 — SomNambul
    Authors: L.A. Bokut, Yuqun Chen, Xueming Deng
    Subjects: Rings and Algebras
    Abstract

    In this paper, we establish the Composition-Diamond lemma for associative
    nonunitary Rota-Baxter algebras with weight $\lambda$. As applications, we
    obtain a linear basis of a free commutative Rota-Baxter algebra without unity,
    show that every countably generated Rota-Baxter algebra with weight 0 can be
    embedded into a two-generated Rota-Baxter algebra and prove the 1/2-PBW
    Theorems for dendriform dialgebra and trialgebra.

  2. Gr\"{o}bner-Shirshov bases and embeddings of algebras.

    Mon, 08/17/2009 - 18:30 — SomNambul
    Authors: L.A. Bokut, Yuqun Chen, Qiuhui Mo
    Subjects: Rings and Algebras
    Abstract

    In this paper, by using Gr\"{o}bner-Shirshov bases, we show that in the
    following classes, each (resp. countably generated) algebra can be embedded
    into a simple (resp. two-generated) algebra: associative differential algebras,
    associative $\Omega$-algebras, associative $\lambda$-differential algebras.

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