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
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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>

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Definition

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

  1. in
  2. There is a series such that

Examples

  1. The additive formal group:
  2. The multiplicative formal group: . In this case, .