Vipul: Created page with "==Definition== Let $R$ be a commutative unital ring. The '''formal power series ring''' over $R$ in one variable, denoted $Rx$ if the..."

2012-07-04T01:59:06Z

Created page with "==Definition== Let <math>R</math> be a commutative unital ring. The '''formal power series ring''' over <math>R</math> in one variable, denoted <math>Rx</math> if the..."

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==Definition==

Let <math>R</math> be a [[commutative unital ring]]. The '''formal power series ring''' over <math>R</math> in one variable, denoted <math>R[[x]]</math> if the variable (indeterminate) is <math>x</math> is the ring whose elements are possibly infinite formal linear combinations of nonnegative integral powers of <math>x</math>, with addition coordinate-wise and multiplication extended <math>R</math>-linearly (infinitely so) from a multiplication of powers that adds up the exponents.

==Related notions==

* [[Laurent series ring]]
* [[Puiseux series ring]]
* [[Hahn series ring]]

Formal power series ring - Revision history

Vipul: Created page with "==Definition== Let R be a commutative unital ring. The '''formal power series ring''' over R in one variable, denoted Rx if the..."

Vipul: Created page with "==Definition== Let $R$ be a commutative unital ring. The '''formal power series ring''' over $R$ in one variable, denoted $Rx$ if the..."