nLab symmetric ring

Idea

A free commutative monoid object in Ab

Definition

Given an abelian group $G$, the symmetric ring is a commutative ring $S(G)$ with an abelian group homomorphism $g:G \to S(G)$, such that for every other commutative ring $R$ with abelian group homomorphism $h:G \to R$, there is a unique commutative ring homomorphism $i:S(G) \to R$ such that $i \circ g = h$.

See also

• commutative ring

• tensor ring

• symmetric algebra