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==== As a ring of formal power series ====
The easiest (though somewhat heavy) construction starts with the ring of [[Formal power series#Power series in several variables|formal power series]] <math>R[[X_1,X_2,...]]</math> over ''R'' in infinitely ([[countably infinite|countably]]) many indeterminates; the elements of this [[power series]] ring are formal infinite sums of terms, each of which consists of a coefficient from ''R'' multiplied by a [[monomial]], where each monomial is a product of finitely many finite powers of indeterminates. One defines Λ<sub>''R''</sub> as its subring consisting of those power series ''S'' that satisfy
#''S'' is invariant under any permutation of the indeterminates, and
#the [[degree of a polynomial|degrees]] of the monomials occurring in ''S'' are bounded.
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