Symmetric Algebra - Module Analog

Module Analog

The construction of the symmetric algebra generalizes to the symmetric algebra S(M) of a module M over a commutative ring. If M is a free module over the ring R, then its symmetric algebra is isomorphic to the polynomial algebra over R whose indeterminates are a basis of M, just like the symmetric algebra of a vector space. However, that is not true if M is not free; then S(M) is more complicated.