Weierstrass preparation theorem: Difference between revisions
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In [[algebra]], the '''Weierstrass preparation theorem''' | {{subpages}} | ||
In [[algebra]], the '''Weierstrass preparation theorem''' describes a canonical form for [[formal power series]] over a [[complete local ring]]. | |||
Let ''O'' be a complete local ring and ''f'' a formal power series in ''O''[[''X'']]. Then ''f'' can be written uniquely in the form | Let ''O'' be a complete local ring and ''f'' a formal power series in ''O''[[''X'']]. Then ''f'' can be written uniquely in the form |
Latest revision as of 13:35, 8 March 2009
In algebra, the Weierstrass preparation theorem describes a canonical form for formal power series over a complete local ring.
Let O be a complete local ring and f a formal power series in O''X''. Then f can be written uniquely in the form
where the bi are in the maximal ideal m of O and u is a unit of O''X''.
The integer n defined by the theorem is the Weierstrass degree of f.
References
- Serge Lang (1993). Algebra, 3rd ed. Addison-Wesley, 208-209. ISBN 0-201-55540-9.