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Unit (ring theory)
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=== Polynomials and power series === For a commutative ring {{mvar|R}}, the units of the [[polynomial ring]] {{math|''R''[''x'']}} are the polynomials <math display="block">p(x) = a_0 + a_1 x + \dots + a_n x^n</math> such that {{math|''a''<sub>0</sub>}} is a unit in {{mvar|R}} and the remaining coefficients <math>a_1, \dots, a_n</math> are [[nilpotent]], i.e., satisfy <math>a_i^N = 0</math> for some {{math|''N''}}.{{sfn|Watkins|2007|loc=Theorem 11.1|ps=}} In particular, if {{mvar|R}} is a [[domain (ring theory)|domain]] (or more generally [[reduced ring|reduced]]), then the units of {{math|''R''[''x'']}} are the units of {{mvar|R}}. The units of the [[power series ring]] <math>R[[x]]</math> are the power series <math display="block">p(x)=\sum_{i=0}^\infty a_i x^i</math> such that {{math|''a''<sub>0</sub>}} is a unit in {{mvar|R}}.{{sfn|Watkins|2007|loc=Theorem 12.1|ps=}}
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