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Let R be the polynomial ring in infinitly many variables x_1,x_2,.... with coefficients in a field...

Let R be the polynomial ring in infinitly many variables x_1,x_2,.... with coefficients in a field F. Let M be the cyclic R- module R itself. Prove that the submodule {x_1,x_2,....} cannot be generated by any finite set.
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