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

Universal enveloping commutative Rota-Baxter algebras of pre- and postcommutative 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 zero weight,precommutative algebras) is not.Comment: 17 p. arXiv admin note: text overlap with arXiv:1708.0016