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math.RA2022
New operated polynomial identities and Gröbner-Shirshov bases
Jinwei Wang, Zhicheng Zhu, Xing Gao
Quite recently, Bremner et al. introduced a new approach to Rota's Classification Problem and classified some (new) operated polynomial identities. In this paper, we prove that all…
math.RA2021
Free weighted (modified) differential algebras, free (modified) Rota-Baxter algebras and Gröbner-Shirshov bases
Zhicheng Zhu, Huhu Zhang, Xing Gao
In this paper, we obtain respectively some new linear bases of free unitary (modified) weighted differential algebras and free nonunitary (modified) Rota-Baxter algebras, in terms…