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J. Algebra Comput."],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:p> In this paper, we obtain, respectively, some new linear bases of free nonunitary (modified) weighted differential algebras and free nonunitary (modified) Rota\u2013Baxter algebras, in terms of the method of Gr\u00f6bner\u2013Shirshov bases. <\/jats:p>","DOI":"10.1142\/s0218196723500352","type":"journal-article","created":{"date-parts":[[2023,5,22]],"date-time":"2023-05-22T01:22:48Z","timestamp":1684718568000},"page":"787-817","source":"Crossref","is-referenced-by-count":1,"title":["Free weighted (modified) differential algebras, free (modified) Rota\u2013Baxter algebras and Gr\u00f6bner\u2013Shirshov bases"],"prefix":"10.1142","volume":"33","author":[{"given":"Zhicheng","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P. R. 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