Gr\"obner-Shirshov bases for Rota-Baxter algebras
classification
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rota-baxteralgebraalgebrasweightapplicationsassociativebasesbasis
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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 and show that every countably generated Rota-Baxter algebra with weight 0 can be embedded into a two-generated Rota-Baxter algebra.
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