Geodesic
Primitive Elements in Symmetric Algebras
Canadian journal of mathematics, Tome 26 (1974) no. 2, pp. 355-364

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Let-R be a commutative ring with 1, and let be the symmetric algebra of an R-module M. We regard the isomorphisms S 0(M) ≅ R and S 1(M) ≅ M a s identifications. There is a unique R-algebra homomorphism Δ : S(M) → S(M) ⊗R S(M) (called the comultiplication) satisfying Δ(m) = m ⊗ 1 + 1 ⊗ m for all m ∊ M; any element x ∊ S(M) for which Δ(x) = x ⊗ 1 + 1 ⊗ x is said to be primitive. The set of all primitive elements in S(M) is denoted P(M). 
Edwards, Gordon. Primitive Elements in Symmetric Algebras. Canadian journal of mathematics, Tome 26 (1974) no. 2, pp. 355-364. doi: 10.4153/CJM-1974-037-1
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     title = {Primitive {Elements} in {Symmetric} {Algebras}},
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