Classification of Rota-Baxter operators on semigroup algebras of order   two and three
  In this paper we determine all the Rota-Baxter operators of weight zero on semigroup algebras of order two and three with the help of computer algebra. We determine the matrices for these Rota-Baxter operators by directly solving the defining equations of the operators. We also produce a Mathematica procedure to predict and verify these solutions. 
Li Guo, Markus Rosenkranz, Shanghua Zheng
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