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Algebra Comput."],"published-print":{"date-parts":[[2020,11]]},"abstract":"<jats:p> Motivated by the formula of partial integration, we introduce the concept of [Formula: see text]-Rota\u2013Baxter algebras, which generalizes the Rota\u2013Baxter algebras introduced by Baxter. We then construct free objects in the category of [Formula: see text]-Rota\u2013Baxter algebras, via a method of Gr\u00f6bner\u2013Shirshov bases. <\/jats:p>","DOI":"10.1142\/s0218196720500447","type":"journal-article","created":{"date-parts":[[2020,7,31]],"date-time":"2020-07-31T04:59:35Z","timestamp":1596171575000},"page":"1359-1373","source":"Crossref","is-referenced-by-count":2,"title":["Free \u03a9-Rota\u2013Baxter algebras and Gr\u00f6bner\u2013Shirshov bases"],"prefix":"10.1142","volume":"30","author":[{"given":"Dan","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P. R. 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