Page "Formal power series" Paragraph 201

Formal power series in any number of indeterminates ( even infinitely many ) can be defined.

If I is an index set and X < sub > I </ sub > is the set of indeterminates X < sub > i </ sub > for i ∈ I, then a monomial X < sup > α </ sup > is any finite product of elements of X < sub > I </ sub > ( repetitions allowed ); a formal power series in X < sub > I </ sub > with coefficients in a ring R is determined by any mapping from the set of monomials X < sup > α </ sup > to a corresponding coefficient c < sub > α </ sub >, and is denoted.

The set of all such formal power series is denoted R < nowiki ></ nowiki > X < sub > I </ sub >< nowiki ></ nowiki >, and it is given a ring structure by defining