# Difference between revisions of "Formal group"

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==Definition== | ==Definition== | ||

− | Let <math>A</math> be a commutative ring. A '''formal group''' in one parameter is a series <math>F\in A[[X,Y]]</math> such that | + | Let <math>A</math> be a commutative ring. A '''formal group''' in one parameter is a [[formal power series]] <math>F\in A[[X,Y]]</math> such that |

#<math>F(X,0)=F(0,X)=X</math> | #<math>F(X,0)=F(0,X)=X</math> | ||

#<math>F(X,Y)=F(Y,X)</math> | #<math>F(X,Y)=F(Y,X)</math> |

## Latest revision as of 18:24, 9 December 2008

## Definition

Let be a commutative ring. A **formal group** in one parameter is a formal power series such that

- in
- There is a series such that

## Examples

- The additive formal group:
- The multiplicative formal group: . In this case, .