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is Is the ring of power series with coefficients in a field free as a module over the polynomials subring?

My question is about freeness ofIs the ring of power series with coefficients in a field free as a module over the polynomials subring.?

is the ring of power series with coefficients in a field free as a module over the polynomials subring?

My question is about freeness of the ring of power series with coefficients in a field over the polynomials subring.

Is the ring of power series with coefficients in a field free as a module over the polynomials subring?

Is the ring of power series with coefficients in a field free as a module over the polynomials subring?

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is the ring of power series with coefficients in a field free as a module over the polynomials subring?

My question is about freeness of the ring of power series with coefficients in a field over the polynomials subring.