Free Rota-Baxter systems and a Hopf algebra structure
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freerota-baxteralgebrahopfstructuresystembasesbasis
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In this paper, we give a linear basis of a free Rota-Baxter system on a set by using the Gr\"{o}bner-Shirshov bases method and then we obtain a left counital Hopf algebra structure on a free Rota-Baxter system.
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