Editing Discrete valuation ring (section)

==== Formal power series ====
Another important example of a DVR is the [[formal power series|ring of formal power series]] <math>R = k[[T]]</math> in one variable <math>T</math> over some field <math>k</math>. The "unique" irreducible element is <math>T</math>, the maximal ideal of <math>R</math> is the principal ideal generated by <math>T</math>, and the valuation <math>\nu</math> assigns to each power series the index (i.e. degree) of the first non-zero coefficient.

If we restrict ourselves to [[real number|real]] or [[complex number|complex]] coefficients, we can consider the ring of power series in one variable that ''converge'' in a neighborhood of 0 (with the neighborhood depending on the power series). This is a discrete valuation ring. This is useful for building intuition with the [[Valuative criterion of properness]].