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Universal enveloping commutative Rota-Baxter algebras of pre- andpostcommutative algebras are constructed. We prove that the pair of varieties(commutative Rota-Baxter algebras of nonzero weight,postcommutative algebras)is a PBW-pair and the pair (commutative Rota-Baxter algebras of zeroweight,precommutative algebras) is not.

Universal enveloping commutative Rota-Baxter algebras of precommutative and postcommutative algebras